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Precalculus

Lesson 1: Reducing rational expressions to lowest terms

Reduce rational expressions to lowest terms: Error analysis

Raiden tried to reduce the following expression to lowest terms:

start fraction, 4, x, squared, minus, 12, x, divided by, 3, x, squared, plus, 15, x, end fraction

This is his work:

Factoring the numerator: 4, x, squared, minus, 12, x, equals, 4, x, left parenthesis, x, minus, 3, right parenthesis

Factoring the denominator: 3, x, squared, plus, 15, x, equals, 3, x, left parenthesis, x, plus, 5, right parenthesis

Reducing to lowest terms:

$\begin{aligned} \dfrac{4x^2-12x}{3x^2+15x}&=\dfrac{4\cancel x(x-3)}{3\cancel x(x+5)} \\\\ &=\dfrac{4(x-3)}{3(x+5)} \end{aligned}$

Finding excluded values: x, does not equal, minus, 5

What mistake did Raiden make?

(Choice A)
He didn't exclude x, equals, 3, which makes the numerator equal to zero.
(Choice B)
He didn't exclude x, equals, 0, which makes the denominator in the original expression equal to zero.
(Choice C)
He excluded x, equals, minus, 5, which doesn't make the numerator equal to zero.
(Choice D)
He didn't factor the numerator correctly.

Stuck?