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Exercises Polynomials and factoring

Example 8.39 from Elementary Algebra, 8.4 Add and Subtract Rational Expressions with Unlike Denominators

Add and Subtract Rational Expressions with Unlike Denominators: example 8.39

Rewrite as equivalent rational expressions with denominator $(x + 1) (x - 3) (x + 3)$ : $\frac{8}{x^{2} - 2 x - 3}, \frac{3 x}{x^{2} + 4 x + 3} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Factor each denominator.

Find the LCD.

Multiply each denominator by the 'missing' factor and multiply each numerator by the same factor.

Simplify the numerators.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Rewrite as equivalent rational expressions with denominator $(x + 3) (x - 4) (x + 4)$ :
$\frac{2}{x^{2} - x - 12}, \frac{1}{x^{2} - 16} .$

How did it go?

PreviousAdd and Subtract Rational Expressions with Unlike Denominators: example 8.38 Next Add and Subtract Rational Expressions with Unlike Denominators: example 8.41

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 8.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.