Question

For the following exercises, find $R\left(x\right)=f\left(x\right).g\left(x\right)$where $f\left(x\right)andg\left(x\right)$are given.

localid="1644679377284" $f\left(x\right)=\frac{6x^2-12x}{x^2+7x-18}andg\left(x\right)=\frac{x^2-81}{3x^2-27x}$

Short answer

The value of$R\left(x\right)=2$

Step-by-step solution

Step 1. Given Information

$f\left(x\right)=\frac{6x^2-12x}{x^2+7x-18}andg\left(x\right)=\frac{x^2-81}{3x^2-27x}$

Step 2. Factor each numerator and denominator

$R\left(x\right)=\frac{6x\left(x-2\right)}{\left(x+9\right)\left(x-2\right)}.\frac{\left(x-9\right)\left(x+9\right)}{3x\left(x-9\right)}$

$R\left(x\right)=\frac{6x\left(x-2\right)\left(x-9\right)\left(x+9\right)}{3x\left(x+9\right)\left(x-2\right)\left(x-9\right)}$

Step 3. Remove common factors and simplify

$R\left(x\right)=\frac{6}{3}=2$