Question

Suppose that `x` and `y` are non zero real numbers such that `(2x+y)/(x-2y)=-3`. What is the value of `(2x^2-4y+8)/(y^2-2x+4)`? A. -1 B. 2 C. 3 D. 4

Answer 1

The answer is `option (B)`

Explanation:

If `(2x+y)/(x-2y)=-3`

Then, cross multiply

`2x+y=-3(x-2y)`

`2x+y=-3x+6y`

`5x=5y`

`x=y`

Therefore, as `y=x`

`(2x^2-4y+8)/(y^2-2x+4)`= `(2(x^2-2x+4))/(x^2-2x+4)`

`(2(cancel(x^2-2x+4)))/cancel(x^2-2x+4)`

`=2`

The answer is `option (B)`