I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.6 : Rational Expressions
12. Perform the indicated operation in the following expression.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}}\]Show All Steps Hide All Steps
Start SolutionWe first need the least common denominator for this rational expression.
\[{\mbox{lcd : }}{\left( {3x + 8} \right)^3}\]Remember that we only take the highest power on each term in the denominator when setting up the least common denominator.
Show Step 2Now multiply each term by an appropriate quantity to get the least common denominator into the denominator of each term.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}} = \frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{{x\left( {3x + 8} \right)}}{{{{\left( {3x + 8} \right)}^2}\left( {3x + 8} \right)}}\] Show Step 3All we need to do now is do the addition and simplify the numerator of the result.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}} = \frac{{x + 10 + 3{x^2} + 8x}}{{{{\left( {3x + 8} \right)}^3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{3{x^2} + 9x + 10}}{{{{\left( {3x + 8} \right)}^3}}}}}\]