If y ≠ 2, which expression is equal to y(y − 2) − 3(y + 2) + 4(y + 6)(y − 2) ?

[m](y^2 - y + 18)/(y − 2)[/m]

If y ≠ 2, which expression is equal to y(y −… | GMAT Sprint

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Algebra

If $y ≠ 2$ , which expression is equal to $\frac{y(y − 2) − 3(y + 2) + 4(y + 6)}{(y − 2)}$ ?

Answer Choices

Correct answer marked below

(y^2 + 22)/(y − 2)

(y^2 + 26)/(y − 2)

(y^2 - y + 18)/(y − 2)

Correct

(y^2 + y + 10)/(y − 2)

10/(y − 2)

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Explanation

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Official Explanation

Official

To simplify the expression:

\frac{y(y - 2) - 3(y + 2) + 4(y + 6)}{y - 2}

Step 1: Expand the numerator

y(y - 2) = y^2 - 2y

-3(y + 2) = -3y - 6

4(y + 6) = 4y + 24

Step 2: Combine the expanded terms

y^2 - 2y - 3y - 6 + 4y + 24

Step 3: Simplify by combining like terms…

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Comments

LFeb 22, 2025

Great question!

DerrickApr 9, 2025

thanksss

AishwaryaApr 8, 2025

thanks

HarshJan 24, 2025

still struggling with these types of problems

KshitizMar 21, 2024

thank you for sharing

KaiFeb 10, 2024

Thank you very much!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

If y≠2y ≠ 2y=2, which expression is equal to y(y−2)−3(y+2)+4(y+6)(y−2)\frac{y(y − 2) − 3(y + 2) + 4(y + 6)}{(y − 2)}(y−2)y(y−2)−3(y+2)+4(y+6)​ ?