What is the highest value of (x^2+3x+4)(x^2+3x+3)?

What is the highest value of (x^2+3x+4)(x^2+3… | GMAT Sprint

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655-705

Algebra

What is the highest value of $\frac{(x^2+3x+4)}{(x^2+3x+3)}$ ?

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Official Explanation

Official

To find the maximum value of

\frac{(x^2+3x+4)}{(x^2+3x+3)}

, we can rewrite it as

\frac{(x^2+3x+3+1)}{(x^2+3x+3)}

which simplifies to

1 + \frac{1}{(x^2+3x+3)}

. To maximize this expression, we need to maximize

\frac{1}{(x^2+3x+3)}

, which occurs when…

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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.

What is the highest value of (x2+3x+4)(x2+3x+3)\frac{(x^2+3x+4)}{(x^2+3x+3)}(x2+3x+3)(x2+3x+4)​?