Suppose that xx and yy are non zero real numbers such that (2x+y)/(x-2y)=-32x+yx2y=3. What is the value of (2x^2-4y+8)/(y^2-2x+4)2x24y+8y22x+4? A. -1 B. 2 C. 3 D. 4

1 Answer
Jun 17, 2018

The answer is option (B)option(B)

Explanation:

If (2x+y)/(x-2y)=-32x+yx2y=3

Then, cross multiply

2x+y=-3(x-2y)2x+y=3(x2y)

2x+y=-3x+6y2x+y=3x+6y

5x=5y5x=5y

x=yx=y

Therefore, as y=xy=x

(2x^2-4y+8)/(y^2-2x+4)2x24y+8y22x+4= (2(x^2-2x+4))/(x^2-2x+4)2(x22x+4)x22x+4

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

=2

The answer is option (B)