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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sub-505

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!

SuraiyaApr 27

easy one, just expand the top and combine like terms. watch the signs on the -3(y+2) part, that's where people slip

SwapnilApr 30

same, I had 26 for a sec until I redid the y terms

HarshiJul 11

thanks, helpful!

HarshiJul 7

wait why is the denominator kept as (y-2) and not multiplied out? like why not just simplify further

MarkusJul 13

look at the answer choices, they all have (y-2) on the bottom so you just leave it

SahajmeetAug 20

the condition y ≠ 2 threw me off for a sec but it's just saying the denominator can't be zero. straightforward after that

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)​ ?