Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{d}{3} + \frac{1}{10d^2}$

View step-by-step help

View step-by-step help

Add and subtract rational expressions

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{d}{3} + \frac{1}{10d^2}

Identify LCD: Identify the least common denominator (LCD) for the fractions. $\newline$ The LCD for the fractions $\frac{d}{3}$ and $\frac{1}{10d^2}$ is $30d^2$ because $30d^2$ is the smallest number that both denominators ( $3$ and $10d^2$ ) can divide into without leaving a remainder.
Rewrite fractions: Rewrite each fraction with the common denominator. $\newline$ To rewrite $\frac{d}{3}$ with the common denominator, multiply both the numerator and the denominator by $10d^2$ . To rewrite $\frac{1}{10d^2}$ with the common denominator, multiply both the numerator and the denominator by $3$ . $\newline$ $\left(\frac{d}{3}\right) \times \left(\frac{10d^2}{10d^2}\right) + \left(\frac{1}{10d^2}\right) \times \left(\frac{3}{3}\right)$ $\newline$ = $\frac{10d^3}{30d^2}$ + $\frac{3}{30d^2}$
Combine fractions: Combine the fractions. $\newline$ Now that both fractions have the same denominator, you can combine them by adding their numerators. $\newline$ $(10d^3 + 3) / 30d^2$
Simplify expression: Simplify the expression, if possible. $\newline$ In this case, the numerator and the denominator do not have any common factors other than $1$ , so the expression is already in its simplest form. $\newline$ $(10d^3 + 3) / 30d^2$

More problems from Add and subtract rational expressions

Question

Evaluate the expression for

t = -4.4

\newline

Write your answer in simplest form.

\newline

` frac{t - 4}{t - 2} =` ____

Posted 1 month ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{g}{3g^2 - 4g}

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\frac{3}{2} - \frac{5p^3}{3}

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{1 + \frac{v^5w}{3}}{1}

\newline

Posted 2 months ago

Question

h

\newline

\frac{-5}{h - 2} = \frac{-4}{h - 3}

\newline

1

2

\newline

h =

h =

Posted 1 month ago

Question

What is the equation of the vertical asymptote of

y = \frac{1}{x + 9}

Posted 2 months ago

Question

What is the excluded value for

y = \frac{1}{x - 9} - 9

\newline

Posted 2 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{9k + 4}{9k^2 + 4k}

\newline

Posted 2 months ago

Question

Divide. Write your answer in simplest form.

\newline

\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)

\newline

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{5 - \frac{3}{t^3}}{1}

\newline

Posted 2 months ago