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

Question

Eva Abramson · Accepted Answer

#5/3#

Trying to identify some common factors to simplify is your aim here.

From the beginning, the reality 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#

Right now, you're utilizing

#5 * y - 5 * 3#

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

#5 * (y - 3)#

Now that you have your attention on the denominator, you can write

#9 = 3 * 3#

Thus, you can write your denominator as

#3 * y - 3 * 3#

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

#3 * (y - 3)#

Reassemble the fraction and use simplification to obtain

#(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#.

Isaiah Anthony · Answer

undefined To simplify the expression (5y-15)/(3y-9), you can factor out a common factor of 5 from the numerator and a common factor of 3 from the denominator. This gives us (5(y-3))/(3(y-3)). Now, we can cancel out the common factor of (y-3) from both the numerator and denominator, resulting in 5/3 as the simplified expression.