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

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Answer 1 · 2016-08-01T11:44:03

$5/3$

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

Right from the start, the fact that we have

$color(purple)("multiple of "y - "something")$

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

$15 = 5 * 3$

You are now working with

$5 * y - 5 * 3$

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

$5 * (y - 3)$

Now focus on the denominator. Notice that you can write

$9 = 3 * 3$

Your denominator can thus be written as

$3 * y - 3 * 3$

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

$3 * (y - 3)$

Put the fraction back together and simplify to get

$(5 * color(red)(cancel(color(black)((y-3)))))/(3 * color(red)(cancel(color(black)((y-3))))) = 5/3$

Keep in mind that you need to have $y != 3$ .

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