If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

[AAPL]

Official Guide

If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

A. -4
B. -1
C. 0
D. 1
E. 2

OA C

[Brent@GMATPrepNow]

Official Guide

If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

A. -4
B. -1
C. 0
D. 1
E. 2

OA C

Given: (4 - x)/(2 + x) = x
Eliminate the fraction by multiplying both sides by (2 + x) to get: (4 - x) = (x)(2 + x)
Expand: 4 - x = 2x + x²
Add x to both sides: 4 = x² + 3x
Subtract 4 from both sides: 0 = x² + 3x - 4

PERFECT! The question asks us to find the value of x² + 3x - 4, and we just showed that the expression equals 0

Answer: C