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#.