Paul's Online Notes
Home / Algebra / Preliminaries / Rational Expressions
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 1-6 : Rational Expressions

4. Perform the indicated operation in the following expression and reduce the answer to lowest terms.

$\frac{{{x^2} + 5x - 24}}{{{x^2} + 6x + 8}}\,\centerdot \,\frac{{{x^2} + 4x + 4}}{{{x^2} - 3x}}$

Show All Steps Hide All Steps

Start Solution

So, we first need to factor each of the polynomials as much as possible.

$\frac{{\left( {x + 8} \right)\left( {x - 3} \right)}}{{\left( {x + 4} \right)\left( {x + 2} \right)}}\,\centerdot \,\frac{{{{\left( {x + 2} \right)}^2}}}{{x\left( {x - 3} \right)}} = \frac{{\left( {x + 8} \right)}}{{\left( {x + 4} \right)}}\,\centerdot \,\frac{{\left( {x + 2} \right)}}{x}$ Show Step 2

Finally, just multiply the two terms together. Doing this gives,

$\frac{{{x^2} + 5x - 24}}{{{x^2} + 6x + 8}}\,\centerdot \,\frac{{{x^2} + 4x + 4}}{{{x^2} - 3x}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{\left( {x + 8} \right)\left( {x + 2} \right)}}{{x\left( {x + 4} \right)}}}}$