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. $\newline$ $\frac{1}{9xy^3} + \frac{2}{9y^5}$

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{1}{9xy^3} + \frac{2}{9y^5}

Identify common denominator: Identify the common denominator. $\newline$ The common denominator for the fractions $\frac{1}{9xy^3}$ and $\frac{2}{9y^5}$ is $9xy^5$ because $y^5$ is the highest power of $y$ present in the denominators and $x$ is present in one of the denominators.
Rewrite with common denominator: Rewrite each fraction with the common denominator. $\newline$ For the first fraction, multiply the numerator and denominator by $y^2$ to get the common denominator: $\newline$ $(\frac{1}{9xy^3}) \cdot (\frac{y^2}{y^2}) = \frac{y^2}{9xy^5}$ $\newline$ For the second fraction, multiply the numerator and denominator by $x$ to get the common denominator: $\newline$ $(\frac{2}{9y^5}) \cdot (\frac{x}{x}) = \frac{2x}{9xy^5}$
Add fractions: Add the fractions with the common denominator. $\newline$ Now that both fractions have the same denominator, we can add them: $\newline$ $\frac{y^2}{9xy^5} + \frac{2x}{9xy^5} = \frac{y^2 + 2x}{9xy^5}$
Simplify expression: Simplify the expression if possible. $\newline$ The expression $(y^2 + 2x)/9xy^5$ is already in its simplest form because the numerator and denominator do not have any common factors that can be canceled out.

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 7 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

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

Posted 5 months ago

Question

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

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

Posted 5 months ago

Question

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

\newline

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

\newline

Posted 5 months ago

Question

h

\newline

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

\newline

1

2

\newline

h =

h =

Posted 7 months ago

Question

What is the equation of the vertical asymptote of

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

Posted 9 months ago

Question

What is the excluded value for

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

\newline

Posted 9 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

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

\newline

Posted 9 months ago

Question

Divide. Write your answer in simplest form.

\newline

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

\newline

Posted 9 months ago

Question

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

\newline

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

\newline

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant