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Math Problems
Algebra 2
Add and subtract rational expressions
Simplify. Express your answer as a single fraction in simplest form.
3
2
−
5
p
3
3
\frac{3}{2} - \frac{5p^3}{3}
2
3
−
3
5
p
3
______
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Parallel Lines (Reasoning and Proof) Page
6
6
6
of
6
6
6
\newline
April
20
20
20
\newline
(
4
4
4
points) In the figure below,
m
∠
1
=
2
x
+
10
,
m
∠
2
=
3
x
+
30
m \angle 1=2 x+10, m \angle 2=3 x+30
m
∠1
=
2
x
+
10
,
m
∠2
=
3
x
+
30
, and
m
∠
3
=
5
x
−
m \angle 3=5 x-
m
∠3
=
5
x
−
Are lines
a
a
a
and
b
b
b
parallel? Show work and explain your reasoning.
\newline
2
x
+
10
2 x+10
2
x
+
10
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(A)
11
c
m
11 \mathrm{~cm}
11
cm
\newline
(B)
10
c
m
10 \mathrm{~cm}
10
cm
\newline
(C)
9
c
m
9 \mathrm{~cm}
9
cm
\newline
(D)
8
c
m
8 \mathrm{~cm}
8
cm
\newline
e to solve.
\newline
Sample question
4
4
4
: degree of difficulty medium
\newline
ays. He earns s a week. How ks of work?
\newline
s
\newline
eeks
\newline
ow many litres
\newline
ow many litres
\newline
(A)
x
+
a
−
b
x+a-b
x
+
a
−
b
\newline
(B)
2
(
a
+
b
)
−
2
x
2(a+b)-2 x
2
(
a
+
b
)
−
2
x
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A triangle has side lengths
=
10
m
,
8
m
,
9
m
=10 \mathrm{~m}, 8 \mathrm{~m}, 9 \mathrm{~m}
=
10
m
,
8
m
,
9
m
\newline
A) Is the triangle a right triangle? (type yes or no in the blank)
\newline
B) Give the number proof for your answer in
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25
25
25
Naomi travels to an interview.
\newline
She travels by car for
1
3
\frac{1}{3}
3
1
of the journey.
\newline
She travels by train for
5
8
\frac{5}{8}
8
5
of the journey.
\newline
She walks for the remaining
500
m
500 \mathrm{~m}
500
m
of the journey.
\newline
Find the length of this journey in kilometres.
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
8
v
2
−
8
\frac{5}{8}v^{2} - 8
8
5
v
2
−
8
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
9
q
+
r
3
\frac{1}{9q} + \frac{r}{3}
9
q
1
+
3
r
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Simplify. Express your answer as a single fraction in simplest form.
\newline
3
y
5
−
10
x
y
3
\frac{3}{y^5} - \frac{10xy}{3}
y
5
3
−
3
10
x
y
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Simplify. Express your answer as a single fraction in simplest form.
\newline
2
9
r
+
5
2
q
3
\frac{2}{9r} + \frac{5}{2q^3}
9
r
2
+
2
q
3
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
6
y
5
5
+
5
6
y
5
z
\frac{6y^5}{5} + \frac{5}{6y^5z}
5
6
y
5
+
6
y
5
z
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
y
3
−
3
5
x
\frac{y}{3} - \frac{3}{5}x
3
y
−
5
3
x
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
4
c
−
2
b
3
\frac{5}{4c} - \frac{2b}{3}
4
c
5
−
3
2
b
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Simplify. Express your answer as a single fraction in simplest form.
\newline
d
3
+
1
10
d
2
\frac{d}{3} + \frac{1}{10d^2}
3
d
+
10
d
2
1
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Simplify. Express your answer as a single fraction in simplest form.
\newline
4
b
4
−
4
9
b
c
4
\frac{4}{b^4} - \frac{4}{9bc^4}
b
4
4
−
9
b
c
4
4
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
4
+
10
s
3
\frac{1}{4} + \frac{10s}{3}
4
1
+
3
10
s
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Simplify. Express your answer as a single fraction in simplest form.
\newline
7
u
v
5
+
1
6
u
\frac{7uv}{5} + \frac{1}{6u}
5
7
uv
+
6
u
1
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Simplify. Express your answer as a single fraction in simplest form.
\newline
4
q
+
1
q
\frac{4}{q} + \frac{1}{q}
q
4
+
q
1
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Simplify. Express your answer as a single fraction in simplest form.
\newline
3
w
5
−
2
3
v
3
w
\frac{3}{w^5} - \frac{2}{3v^3w}
w
5
3
−
3
v
3
w
2
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Simplify. Express your answer as a single fraction in simplest form.
\newline
4
b
c
+
4
b
c
\frac{4}{bc} + \frac{4}{bc}
b
c
4
+
b
c
4
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Simplify. Express your answer as a single fraction in simplest form.
\newline
u
v
4
5
u
v
−
2
5
u
v
\frac{uv^4}{5uv} - \frac{2}{5uv}
5
uv
u
v
4
−
5
uv
2
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Simplify. Express your answer as a single fraction in simplest form.
\newline
8
z
3
−
5
3
\frac{8z}{3} - \frac{5}{3}
3
8
z
−
3
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
7
u
2
+
u
4
\frac{7u}{2} + \frac{u}{4}
2
7
u
+
4
u
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Simplify. Express your answer as a single fraction in simplest form.
\newline
t
2
u
4
+
t
3
\frac{t^2u}{4} + \frac{t}{3}
4
t
2
u
+
3
t
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Simplify. Express your answer as a single fraction in simplest form.
\newline
3
b
3
−
b
2
3
\frac{3b}{3} - \frac{b^2}{3}
3
3
b
−
3
b
2
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Simplify. Express your answer as a single fraction in simplest form.
\newline
q
r
5
+
q
5
r
4
4
\frac{qr}{5} + \frac{q^5r^4}{4}
5
q
r
+
4
q
5
r
4
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Simplify. Express your answer as a single fraction in simplest form.
\newline
x
3
+
5
w
x
3
\frac{x}{3} + \frac{5}{wx^3}
3
x
+
w
x
3
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
r
2
+
r
s
3
\frac{r}{2} + \frac{rs}{3}
2
r
+
3
rs
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Simplify. Express your answer as a single fraction in simplest form.
\newline
2
3
+
5
a
b
2
\frac{2}{3} + \frac{5ab}{2}
3
2
+
2
5
ab
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
q
2
+
3
q
5
\frac{5}{q^2} + \frac{3q}{5}
q
2
5
+
5
3
q
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Simplify. Express your answer as a single fraction in simplest form.
\newline
4
5
−
x
5
\frac{4}{5} - \frac{x}{5}
5
4
−
5
x
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Simplify. Express your answer as a single fraction in simplest form.
\newline
7
y
3
5
−
7
y
z
5
5
\frac{7y^3}{5} - \frac{7yz^5}{5}
5
7
y
3
−
5
7
y
z
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
2
r
s
−
r
3
s
5
3
\frac{2}{rs} - \frac{r^3s^5}{3}
rs
2
−
3
r
3
s
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
7
u
2
v
3
+
1
3
\frac{1}{7u^2v^3} + \frac{1}{3}
7
u
2
v
3
1
+
3
1
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Simplify. Express your answer as a single fraction in simplest form.
\newline
z
5
−
3
10
z
\frac{z}{5} - \frac{3}{10}z
5
z
−
10
3
z
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Simplify. Express your answer as a single fraction in simplest form.
\newline
v
5
+
9
u
5
\frac{v}{5} + \frac{9u}{5}
5
v
+
5
9
u
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
4
−
4
9
r
s
\frac{1}{4} - \frac{4}{9rs}
4
1
−
9
rs
4
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Simplify. Express your answer as a single fraction in simplest form.
\newline
9
u
2
3
u
v
−
2
3
u
v
\frac{9u^2}{3uv} - \frac{2}{3uv}
3
uv
9
u
2
−
3
uv
2
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
2
−
b
c
5
\frac{5}{2} - \frac{bc}{5}
2
5
−
5
b
c
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Simplify. Express your answer as a single fraction in simplest form.
\newline
2
5
+
9
u
5
\frac{2}{5} + \frac{9u}{5}
5
2
+
5
9
u
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Simplify. Express your answer as a single fraction in simplest form.
\newline
r
s
2
3
−
3
s
\frac{rs^2}{3} - \frac{3}{s}
3
r
s
2
−
s
3
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Simplify. Express your answer as a single fraction in simplest form.
\newline
8
w
x
5
−
5
w
\frac{8wx}{5} - \frac{5}{w}
5
8
w
x
−
w
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
4
+
7
x
4
\frac{1}{4} + \frac{7x}{4}
4
1
+
4
7
x
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Simplify. Express your answer as a single fraction in simplest form.
\newline
c
5
2
−
d
3
\frac{c^5}{2} - \frac{d}{3}
2
c
5
−
3
d
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Simplify. Express your answer as a single fraction in simplest form.
\newline
t
u
4
−
6
t
u
3
5
\frac{tu}{4} - \frac{6tu^3}{5}
4
t
u
−
5
6
t
u
3
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Simplify. Express your answer as a single fraction in simplest form.
\newline
4
p
2
q
5
p
q
+
5
p
q
\frac{4p^2q^5}{pq} + \frac{5}{pq}
pq
4
p
2
q
5
+
pq
5
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
2
−
v
w
4
\frac{5}{2} - \frac{vw}{4}
2
5
−
4
v
w
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Simplify. Express your answer as a single fraction in simplest form.
\newline
1
2
+
q
4
3
\frac{1}{2} + \frac{q^4}{3}
2
1
+
3
q
4
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Simplify. Express your answer as a single fraction in simplest form.
\newline
7
q
3
−
3
5
\frac{7q}{3} - \frac{3}{5}
3
7
q
−
5
3
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Simplify. Express your answer as a single fraction in simplest form.
\newline
5
4
+
2
q
4
\frac{5}{4} + \frac{2}{q^4}
4
5
+
q
4
2
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Simplify. Express your answer as a single fraction in simplest form.
\newline
7
w
x
5
4
−
4
7
x
3
\frac{7wx^5}{4} - \frac{4}{7x^3}
4
7
w
x
5
−
7
x
3
4
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1
2
3
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