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Exercises Polynomials and factoring

Example 8.36 from Elementary Algebra, 8.3 Add and Subtract Rational Expressions with a Common Denominator

Add and Subtract Rational Expressions with a Common Denominator: example 8.36

Add: $\frac{4 u - 1}{3 u - 1} + \frac{u}{1 - 3 u} .$

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

The denominators are opposites, so multiply the second fraction by $\frac{−1}{−1}$ .

Simplify the second fraction.

The denominators are the same. Add the numerators.

Simplify.

Simplify.

Your turn

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

Add: $\frac{8 x - 15}{2 x - 5} + \frac{2 x}{5 - 2 x} .$

How did it go?

PreviousAdd and Subtract Rational Expressions with a Common Denominator: example 8.35 Next Add and Subtract Rational Expressions with a Common Denominator: example 8.37

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 8.3, 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.