# How do you simplify (5y-15)/(3y-9)?

Aug 1, 2016

$\frac{5}{3}$

#### Explanation:

Your goal here is to see if you can find some common factors to simplify.

Right from the start, the fact that we have

$\textcolor{p u r p \le}{\text{multiple of "y - "something}}$

in the numerator and in the denominator is promising. Start by looking at the numerator. Notice that you can write $15$ as

$15 = 5 \cdot 3$

You are now working with

$5 \cdot y - 5 \cdot 3$

Since $5$ is a common factor here, you can rewrite this as

$5 \cdot \left(y - 3\right)$

Now focus on the denominator. Notice that you can write

$9 = 3 \cdot 3$

Your denominator can thus be written as

$3 \cdot y - 3 \cdot 3$

Since $3$ is a common factor, you can rewrite this as

$3 \cdot \left(y - 3\right)$

Put the fraction back together and simplify to get

$\frac{5 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(y - 3\right)}}}}{3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(y - 3\right)}}}} = \frac{5}{3}$

Keep in mind that you need to have $y \ne 3$.