Solve : (3y-8)/(5y-2) = (y-2)/(y+5) ?

1 Answer
Apr 8, 2018

y=11/2 or y=4

Explanation:

In the equation (3y-8)/(5y-2)=(y-2)/(y+5), w have uin the denominator 5y-2 andy+5. Asdenominator cannot be zero, we cannot have y=2/5 or y=-5.

Multiplying each side of (3y-8)/(5y-2)=(y-2)/(y+5) by (5y-2)(y+5), we get

(3y-8)(y+5)=(y-2)(5y-2)

or 3y^2+7y-40=5y^2-12y+4

or 2y^2-19y+44=0

or 2y^2-8y-11y+44=0

or 2y(y-4)-11(y-4)=0

or (2y-11)(y-4)=0

i.e. either 2y-11=0 i.e. y=11/2

or y-4=0 i.e. y=4

Observe that none of the solution is y=2/5 or y=-5, which are notin domain. Hence our solution is y=11/2 or y=4.