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Exercises Expressions, exponents and radicals

Example 4 from Algebra and Trigonometry, 1.6 Rational Expressions

Adding Rational Expressions

Add the rational expressions:

\frac{5}{x} + \frac{6}{y}

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
First, we have to find the LCD. In this case, the LCD will be $x y .$ We then multiply each expression by the appropriate form of 1 to obtain $x y$ as the denominator for each fraction.

$\begin{array}{l} \frac{5}{x} \cdot \frac{y}{y} + \frac{6}{y} \cdot \frac{x}{x} \\ \frac{5 y}{x y} + \frac{6 x}{x y} \end{array}$

Now that the expressions have the same denominator, we simply add the numerators to find the sum.

$\frac{6 x + 5 y}{x y}$

How did it go?

PreviousDividing Rational Expressions Next Subtracting Rational Expressions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.6, 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.