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Section 1-6 : Rational Expressions

1. Reduce the following rational expression to lowest terms.

\[\frac{{{x^2} - 6x - 7}}{{{x^2} - 10x + 21}}\]

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Start Solution

First, we need to factor the numerator and denominator as much as we can. Doing that gives,

\[\frac{{{x^2} - 6x - 7}}{{{x^2} - 10x + 21}} = \frac{{\left( {x - 7} \right)\left( {x + 1} \right)}}{{\left( {x - 7} \right)\left( {x - 3} \right)}}\] Show Step 2

Now all we need to do is cancel all the factors that we can in order to reduce the rational expression to lowest terms.

\[\frac{{{x^2} - 6x - 7}}{{{x^2} - 10x + 21}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{x + 1}}{{x - 3}}}}\]