If a + c ≠ b, then [4a²−(a + b − c)²]/[a − b + c] = A) a - b - c B) a + b - c C) 3a - b - c D) 3a + b + c E) 3a + b - c Answer: E

Brent@GMATPrepNow wrote:If a + c ≠ b, then [4a²−(a + b − c)²]/[a − b + c] = A) a - b - c B) a + b - c C) 3a - b - c D) 3a + b + c E) 3a + b - c Answer: E Pick some easy numbers: a=1,b=2,c=3 Plug into original equation with the result = 2 Sub same values into the answer choices and see which yields 2: A. Result -4 fails B. " 0 fails C. " -2 fails D. " 8 fails E. " 2 Winner

Brent@GMATPrepNow wrote:If a + c ≠ b, then [4a²−(a + b − c)²]/[a − b + c] = A) a - b - c B) a + b - c C) 3a - b - c D) 3a + b + c E) 3a + b - c Answer: E Here's an algebraic approach First recognize that 4a² = (2a)² So, the numerator can be written as (2a)² − (a + b − c)² This happens to be a difference of squares So, we can factor the the numerator as follows: [2a + (a + b − c)][2a - (a + b − c)] Simplify to get: [3a + b − c][a - b + c)] So, the given fraction becomes [3a + b − c][a - b + c)]/[a − b + c] This simplifies to be: 3a + b − c Answer: E Cheers, Brent

Another approach! Let's say that [4a²-(a + b - c)²]/[a - b + c] = x 4a² - (a + b - c)² = (a - b + c) * x We know that 4a² - a² on the left is going to give us 3a², so we must have a 3a term on the right hand side. We know that - (-c)² is going to give us -c², so we must have +c * -c, or -c on the right hand side. We know that - (+b)² is going to give us -b², so we must have -b * +b, or +b on the right hand side. From there, our answer can only be 3a + b - c!

My answer above is obviously much less cool (and less useful!) than Brent's, but I did want to show a way to bash your way out of the problem under test conditions if you're stuck. (Alas, the elegant answer doesn't always arrive in time!)