Q3. - Algebra 1

Question

Find each product or quotient.

$\frac{\left(x+6\right)\left(x-2\right)}{x^3}\cdot \frac{7x^2}{x-3}$

Step-by-Step Solution

Answer

$\frac{7x^2+28x-84}{x^2-3x}$

Step 1. Multiplying rational expression.

Let $x,y,z$ and $w$ be polynomials with $y,w\ne 0$, then, $\frac{x}{y}\cdot \frac{z}{w}=\frac{xz}{yw}$.

Step 2. Divide.

Divide by the common factors before multiplying.

$\frac{\left(x+6\right)\left(x-2\right)}{x^3}\cdot \frac{7x^2}{\left(x-3\right)}=\frac{7\left(x+6\right)\left(x-2\right)}{x\left(x-3\right)}$

Step 3. Simplify.

Simplify the above obtained expression.

$\frac{7x^2-14x+42x-84}{x^2-3x}=\frac{7x^2+28x-84}{x^2-3x}$

The product of given expression is $\frac{7x^2+28x-84}{x^2-3x}$.