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Chapter 7: Problem 79

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{x}+\frac{y+1}{y}$$

Short Answer

Expert verified
The simplified expression is 2.

Step by step solution

01

Identity Denominators

In this problem, denominators are different. They are 'x' and 'y' respectively.
02

Finding Common Denominator

A common denominator for two fractions can be found by multiplying the two denominators. So the common denominator here is 'xy'.
03

Converting to Common Denominator

Rewriting both fractions with the common denominator results to \[(x-1)\frac{y}{xy} + (y+1)\frac{x}{xy} = \frac{y(x-1)+x(y+1)}{xy}\]
04

Simplification

Expanding and simplifying the numerator we get \[(yx-y+xy+x) = \frac{xy+yx+x-y}{xy} = \frac{2xy}{xy}\]
05

Final Simplification

In the fraction \(\frac{2xy}{xy}\), 'xy' in the numerator and the denominator cancel each out leaving the final simplified result.

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Most popular questions from this chapter

Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{10}{x-2}-\frac{6}{2-x}$$

Explain how to add rational expressions when denominators are opposites. Use an example to support your explanation.

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{6}+\frac{x+2}{3}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$
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