Q11. - Algebra 1

Question

Simplify the complex fraction. Show your work.

$\frac{\frac{5}{x-3}}{\frac{x-6}{x^2-x-6}}$

Step-by-Step Solution

Answer

The simplified complex fraction is $\frac{5\left(x+2\right)}{x-6}$. 

Step 1. State the concept of complex fractions.

In a complex fraction, $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$, wherein there are one or more fractions in the numerator and denominator where $a, b, c,$ and $d$ can be numbers or polynomials.

Step 2. Simplify the expression by multiplying with the reciprocal.

First, multiply the numerator with the reciprocal of the denominator and then further simplify.

$$\begin{gathered} \frac{\frac{5}{x-3}}{\frac{x-6}{x^2-x-6}}=\frac{5}{x-3}÷\frac{x-6}{x^2-x-6} \\ =\frac{5}{x-3}\times \frac{x^2-x-6}{x-6} \end{gathered}$$

Step 3. Simplify the expression.

To further simplify factor $x^2-x-6$ and cancel out the common terms.