Check the solution to "Simplify a Complex Rational Expression by Writing It..."

Ramsey

Answered question

2021-09-15

Simplify a Complex Rational Expression by Writing It as Division. In the following exercises, simplify

\frac{x - \frac{3 x}{x + 5}}{\frac{1}{x + 5} + \frac{1}{x - 5}}

Lacey-May Snyder

Skilled2021-09-16Added 88 answers

Step 1
Given:

\frac{x - \frac{3 x}{x + 5}}{\frac{1}{x + 5} - \frac{1}{x - 5}}

\frac{1}{x + 5} + \frac{1}{x - 5} = \frac{2 x}{(x + 5) (x - 5)}

= \frac{x - \frac{3 x}{x + 5}}{\frac{2 x}{(x + 5) (x - 5)}}

x - \frac{3 x}{x + 5} = \frac{x^{2} + 2 x}{x + 5}

= \frac{\frac{x^{2} + 2 x}{x + 5}}{\frac{2 x}{(x + 5) (x - 5)}}

Step 2

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \frac{d}{c}

= \frac{(x^{2} + 2 x) (x + 5) (x - 5)}{(x + 5) 2 x}

Now cancel the common factor

(x + 5)

we get,

\frac{(x^{2} + 2 x) (x - 5)}{2 x}

Factor

(x^{2} + 2 x)

x (x + 2)

Step 3

= \frac{x (x + 2) (x - 5)}{2 x}

By canceling the common factor x,

\Rightarrow \frac{(x + 2) (x - 5)}{2}

\Rightarrow \frac{x - \frac{3 x}{x + 5}}{\frac{1}{x + 5} - \frac{1}{x - 5}} = \frac{(x + 2) (x - 5)}{2}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?