Suppose x = a/b (b≠0). Which of following is equivalent to

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[GMAT math practice question]

Suppose x = a/b (b≠0). Which of following is equivalent to (a^2+ab) / (a^2+b^2)?

A. (x^2+x)/(x^2+1)
B. 1/(x^2+1)
C. 1
D. x^2+1
E. x^2+x

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by GMATGuruNY » Thu Apr 25, 2019 3:08 am
Max@Math Revolution wrote:[GMAT math practice question]

Suppose x = a/b (b≠0). Which of following is equivalent to (a^2+ab) / (a^2+b^2)?

A. (x^2+x)/(x^2+1)
B. 1/(x^2+1)
C. 1
D. x^2+1
E. x^2+x
Let a=2 and b=1, with the result that x = a/b = 2/1 = 2 and that (a²+ab)/(a²+b²) = (4+2)/(4+1) = 6/5.
The correct answer must yield 6/5 when x=2.
Only A works:
(x²+x)/(x²+1) = (4+2)/(4+1) = 6/5

The correct answer is A.
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by Max@Math Revolution » Mon Apr 29, 2019 5:14 pm
=>

(a^2+ab) / (a^2+b^2)?
= { (a^2/b^2) + (ab/b^2) } / { (a^2/b^2) + (b^2/b^2) }
= { (a/b)^2 + (a/b) } / { (a/b)^2 + 1 }
= (x^2+x)/(x^2+1)

Therefore, the answer is A.
Answer: A