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
5. Perform the indicated operation in the following expression and reduce the answer to lowest terms.
\[\frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}} \div \frac{{{x^2} - x - 42}}{{{x^2} + 7x + 6}}\]Show All Steps Hide All Steps
Start SolutionSo, we first need to do is convert this into a product.
\[\frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}} \div \frac{{{x^2} - x - 42}}{{{x^2} + 7x + 6}} = \frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}}\,\centerdot \,\frac{{{x^2} + 7x + 6}}{{{x^2} - x - 42}}\]Make sure that you don’t do the factoring and canceling until you’ve converted the division to a product.
Show Step 2Now we can factor each of the terms as much as possible to get,
\[\frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}} \div \frac{{{x^2} - x - 42}}{{{x^2} + 7x + 6}} = \frac{{\left( {x - 7} \right)\left( {x + 7} \right)}}{{\left( {2x - 5} \right)\left( {x + 1} \right)}}\centerdot \frac{{\left( {x + 1} \right)\left( {x + 6} \right)}}{{\left( {x - 7} \right)\left( {x + 6} \right)}}\] Show Step 3Finally cancel as much as possible to reduce to lowest terms and do the product.
\[\frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}} \div \frac{{{x^2} - x - 42}}{{{x^2} + 7x + 6}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{x + 7}}{{2x - 5}}}}\]