QuestionAugust 24, 2025

Multiply. (x^2-x-6)/(x^2)+x-6cdot (x-2)/(4x-12) Simplify your answer as much as possible. square

Multiply. (x^2-x-6)/(x^2)+x-6cdot (x-2)/(4x-12) Simplify your answer as much as possible. square
Multiply. (x^2-x-6)/(x^2)+x-6cdot (x-2)/(4x-12) Simplify your answer as much as possible. square

Solution
4.4(308 votes)

Answer

\frac{x+2}{4(x+3)} Explanation 1. Factor the expressions Factor \frac{x^{2}-x-6}{x^{2}+x-6} as \frac{(x-3)(x+2)}{(x+3)(x-2)}. Factor \frac{x-2}{4x-12} as \frac{x-2}{4(x-3)}. 2. Cancel common factors Cancel (x-3) and (x-2) from numerator and denominator. 3. Simplify the expression The simplified expression is \frac{x+2}{4(x+3)}.

Explanation

1. Factor the expressions<br /> Factor $\frac{x^{2}-x-6}{x^{2}+x-6}$ as $\frac{(x-3)(x+2)}{(x+3)(x-2)}$. Factor $\frac{x-2}{4x-12}$ as $\frac{x-2}{4(x-3)}$.<br />2. Cancel common factors<br /> Cancel $(x-3)$ and $(x-2)$ from numerator and denominator.<br />3. Simplify the expression<br /> The simplified expression is $\frac{x+2}{4(x+3)}$.
Click to rate:

Similar Questions