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Algebra Problem

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Algebra Problem

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Is the first step to this problem to multiply by x to get rid of the denominator? I did this and was able to get 1-x^2+ x = y but I have no idea what to do next.

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GMAT/MBA Expert

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Hi sgraves,

You've made a slight math error in your work - you have to multiply EVERY "piece" by X (and you didn't do that). If you redo that step, then you'll end up with:

1 - X^2 + X^2 = Y. The X-terms will cancel out and you'll be left with 1=Y

In addition, you could solve this question by TESTing VALUES. Try TESTing X=1 OR X=2 and solve for Y.

GMAT assassins aren't born, they're made,
Rich

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Quote:
If x ≠ 0, and (1 - x²)/x + x = y/x, then y =

A) 1
B) 2
C) 3
D) 4
E) 5
Given: (1 - x²)/x + x = y/x
Multiply both sides by x to get: (1 - x²) + x² = y
Simplify: 1 = y

Answer: A

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- Eliminating fractions in equations: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/video/963

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sgraves wrote:
Is the first step to this problem to multiply by x to get rid of the denominator? I did this and was able to get 1-x^2+ x = y but I have no idea what to do next.
To start, we can multiply the given equation by x (possible since x ≠ 0) and we have:

1 - x^2 + x^2 = y

Since the x^2 values cancel out, we are left with: 1 = y.

Answer: A

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You're doing it (mostly) right! Multiplying both sides by x gives:

x * ((1 - x²)/x + x) = x * (y/x)

or

x * (1 - x²)/x + x * x = y

You forgot the part in blue, but that's a very easy mistake to make! Don't sweat it, it happens to me too.

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