Q4. - Algebra 1

Question

Find each product or quotient.

$\frac{\left(x+3\right)}{y^2}÷\frac{x^2-9}{y}$

Step-by-Step Solution

Answer

$\frac{1}{y\left(x-3\right)}$

Step 1. Dividing rational expression.

Let $x,y,z$ and $w$ be polynomials with $y,z,w\ne 0$, then, $\frac{x}{y}÷\frac{z}{w}=\frac{x}{y}\cdot \frac{w}{z}=\frac{xw}{yz}$.

Step 2. Divide.

Divide by the common factors.

$\frac{\left(x+3\right)}{y^2}÷\frac{x^2-9}{y}=\frac{\left(x+3\right)}{y^2}\cdot \frac{y}{x^2-9}$

Step 3. Simplify.

Simplify the above obtained expression.

$\begin{array}{c}\frac{\left(x+3\right)y}{y^2\left(x^2-9\right)}=\frac{\left(x+3\right)}{y\left(x+3\right)\left(x-3\right)}\\ =\frac{1}{y\left(x-3\right)}\end{array}$

The product of given expression is $\frac{1}{y\left(x-3\right)}$.