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Algebra 2
Name
Damie Taidrik
ID: 1
Rational Expressions / Equations QUIZ
Date 
5//3//2024 Period 8


(p^(2)-6p-27)/(p^(2)-17 p+72)
A) 
(p-8)/(p+3);{9,-3}
B) 
(9p^(2))/(p+8);{1,-8}
C) 
(7(p+1))/(5p+6);{-(6)/(5)}
D) 
(p+3)/(p-8);{9,8}

Simplify each expression.
2) 
(2)/(b+1)+(3)/(b-5)
A) 
(18 b+5-2b^(2))/(6b(b-1))
B) 
(23 b+5-4b^(2))/(6b(b-1))
C) 
(15 b+5-2b^(2))/(6b(b-1))
3) 
(6)/(n-2)-(5)/(n+3)
A) 
(25-4n^(3)+12n^(2))/(10 n)
B) 
(n+28)/((n-2)(n+3))
D) 
(5b-7)/((b-5)(b+1))
C) 
(2)/(n-10)
D) 
(2+n)/(n-10)
4) 
(7n)/(3n^(2)-12 n-15)*(9n^(2)-18 n-27)/(3n-9)
5) 
(18 n-12)/(6n^(2)+2n-4)÷(n+3)/(2n+2)
A) 
(7n)/(n-5)
B) 
(4(n+4))/(n-6)
A) 9
B) 
(6)/(n+3)
C) 
(6n)/(n+5)
D) 
(n+4)/(6)
C) 
(n-2)/(10 n)
D) 
(3)/(n+3)

Algebra 22\newlineName\newlineDamie Taidrik\newlineID: 11\newlineRational Expressions / Equations QUIZ\newlineDate \newline55//33//20242024 Period 88\newlinep26p27p217p+72\frac{p^{2}-6p-27}{p^{2}-17 p+72}\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}\newlineB) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}\newlineC) \newline7(p+1)5p+6;{65}\frac{7(p+1)}{5p+6};\left\{-\frac{6}{5}\right\}\newlineD) \newlinep+3p8;{9,8}\frac{p+3}{p-8};\{9,8\}\newlineSimplify each expression.\newline22) \newline2b+1+3b5\frac{2}{b+1}+\frac{3}{b-5}\newlineA) \newline18b+52b26b(b1)\frac{18 b+5-2b^{2}}{6b(b-1)}\newlineB) \newline23b+54b26b(b1)\frac{23 b+5-4b^{2}}{6b(b-1)}\newlineC) \newline15b+52b26b(b1)\frac{15 b+5-2b^{2}}{6b(b-1)}\newline33) \newline6n25n+3\frac{6}{n-2}-\frac{5}{n+3}\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}00\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}11\newlineD) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}22\newlineC) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}33\newlineD) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}44\newline44) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}55\newline55) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}66\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}77\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}88\newlineA) 99\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}99\newlineC) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}00\newlineD) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}11\newlineC) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}22\newlineD) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}33

Full solution

Q. Algebra 22\newlineName\newlineDamie Taidrik\newlineID: 11\newlineRational Expressions / Equations QUIZ\newlineDate \newline55//33//20242024 Period 88\newlinep26p27p217p+72\frac{p^{2}-6p-27}{p^{2}-17 p+72}\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}\newlineB) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}\newlineC) \newline7(p+1)5p+6;{65}\frac{7(p+1)}{5p+6};\left\{-\frac{6}{5}\right\}\newlineD) \newlinep+3p8;{9,8}\frac{p+3}{p-8};\{9,8\}\newlineSimplify each expression.\newline22) \newline2b+1+3b5\frac{2}{b+1}+\frac{3}{b-5}\newlineA) \newline18b+52b26b(b1)\frac{18 b+5-2b^{2}}{6b(b-1)}\newlineB) \newline23b+54b26b(b1)\frac{23 b+5-4b^{2}}{6b(b-1)}\newlineC) \newline15b+52b26b(b1)\frac{15 b+5-2b^{2}}{6b(b-1)}\newline33) \newline6n25n+3\frac{6}{n-2}-\frac{5}{n+3}\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}00\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}11\newlineD) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}22\newlineC) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}33\newlineD) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}44\newline44) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}55\newline55) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}66\newlineA) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}77\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}88\newlineA) 99\newlineB) \newlinep8p+3;{9,3}\frac{p-8}{p+3};\{9,-3\}99\newlineC) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}00\newlineD) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}11\newlineC) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}22\newlineD) \newline9p2p+8;{1,8}\frac{9p^{2}}{p+8};\{1,-8\}33
  1. Factorize Numerator/Denominator: Factorize the numerator and denominator.\newlineNumerator: p26p27=(p9)(p+3)p^2 - 6p - 27 = (p - 9)(p + 3)\newlineDenominator: p217p+72=(p9)(p8)p^2 - 17p + 72 = (p - 9)(p - 8)
  2. Cancel Common Factors: Cancel out the common factors.\newline(p9)(p+3)/(p9)(p8)=(p+3)/(p8)(p - 9)(p + 3) / (p - 9)(p - 8) = (p + 3) / (p - 8)
  3. Identify Restrictions: Identify the restrictions where the original expression is undefined.\newlinep9p \neq 9 (makes the factor (p9)(p - 9) zero in the denominator)\newlinep8p \neq 8 (makes the factor (p8)(p - 8) zero in the denominator)

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