Chapter 11.4, Problem 51PPE

To determine

Simplify the complex fraction

Answer to Problem 51PPE

  $\frac{-4x}{3+xy}$

Explanation of Solution

Given:

The complex fraction

  $\frac{-4}{\frac{3}{x}+y}$

Concept Used:

• To divide two fractions, flip the second fraction and multiply it with the first fraction,

$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}$

Calculation:

In order to simplify the given expression, first simplify the fractions in numerator and denominator and then flip the denominator fraction and multiply as shown below,

  $\begin{array}{c}\frac{-4}{\frac{3}{x}+y}=\frac{-4}{\frac{3+xy}{x}}\\ =\frac{-4}{3+xy}\cdot x\\ =\frac{-4x}{3+xy}\end{array}$

Thus, the given complex fraction simplifies to $\frac{-4x}{3+xy}$.