How do you solve 2/3+5/(y-4)=(y+6)/(3y-12) and find any extraneous solutions?

1 Answer
Nov 24, 2017

y=-1 and the solution is not extraneous.

Explanation:

First, find the LCM between 3, y-4, and 3y-12. In this case, it is 3y-12. Then change the fractions so that they share a common denominator. This yields

(2/3)xx((y-4)/(y-4))+(5/(y-4))xx(3/3)= (y+6)/(3y-12)

After simplifying, you get

(2y-8)/(3y-12) + 15/(3y-12) = (y+6)/(3y-12)

Multiply both sides by 3y-12 to get

2y-8+15=y+6

Simplify

2y+7=y+6

Subtract both sides by 7, then subtract both sides by y to get

y=-1

Check whether this is extraneous by plugging in -1 to the original equation. If you do, you get

-1/3=-1/3

Therefore, our solution is not extraneous.