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Section 1.6 : Rational Expressions

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

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

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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,

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