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

1 Answer
Jun 17, 2018

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)