If $y=\frac{|3 x-5|}{-x^{2}-3}$, for what value of... | Free GMAT Practice Question | GMAT Panda

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If y = \frac{∣3 x - 5∣}{- x ^{2} - 3}, for what value of x will the value of y be greatest?

Explanation	Calculations	Help
$We factor out the negative sign from the denominator to simplify the expression.$	$y = \frac{∣ 3 x - 5 ∣}{- x ^{2} - 3} = - \frac{∣ 3 x - 5 ∣}{x ^{2} + 3}$
$We note that the denominator is always positive, so including the negative sign makes it negative.$	$x^{2} + 3 > 0 - (x^{2} + 3) < 0$
$We see that y cannot be positive, so its highest value is zero, which happens when the numerator equals zero.$	$∣ 3 x - 5 ∣ = 0 3 x - 5 = 0 3 x = 5 x = \frac{5}{3}$	Theory & Tactics Method Card ALG5-B Click to view full details Theory & Tactics Method Card EQUA1-A Click to view full details

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\frac{5}{3}

If y = \frac{∣3 x - 5∣}{- x ^{2} - 3}, for what value of x will the value of y be greatest?

Explanation	Calculations	Help
$We factor out the negative sign from the denominator to simplify the expression.$	$y = \frac{∣ 3 x - 5 ∣}{- x ^{2} - 3} = - \frac{∣ 3 x - 5 ∣}{x ^{2} + 3}$
$We note that the denominator is always positive, so including the negative sign makes it negative.$	$x^{2} + 3 > 0 - (x^{2} + 3) < 0$
$We see that y cannot be positive, so its highest value is zero, which happens when the numerator equals zero.$	$∣ 3 x - 5 ∣ = 0 3 x - 5 = 0 3 x = 5 x = \frac{5}{3}$	Theory & Tactics Method Card ALG5-B Click to view full details Theory & Tactics Method Card EQUA1-A Click to view full details

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\frac{5}{3}