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Section 1.6 : Rational Expressions
2. Reduce the following rational expression to lowest terms.
\[\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}}\]Show All Steps Hide All Steps
Start SolutionFirst, we need to factor the numerator and denominator as much as we can. Doing that gives,
\[\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} = \frac{{{{\left( {x + 3} \right)}^2}}}{{\left( {x + 3} \right)\left( {x - 3} \right)}}\] Show Step 2Now all we need to do is cancel all the factors that we can in order to reduce the rational expression to lowest terms.
\[\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{x + 3}}{{x - 3}}}}\]