Problem 79
Question
Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{x}+\frac{y+1}{y}$$
Step-by-Step Solution
Verified Answer
The simplified expression is 2.
1Step 1: Identity Denominators
In this problem, denominators are different. They are 'x' and 'y' respectively.
2Step 2: Finding Common Denominator
A common denominator for two fractions can be found by multiplying the two denominators. So the common denominator here is 'xy'.
3Step 3: Converting to Common Denominator
Rewriting both fractions with the common denominator results to \[(x-1)\frac{y}{xy} + (y+1)\frac{x}{xy} = \frac{y(x-1)+x(y+1)}{xy}\]
4Step 4: Simplification
Expanding and simplifying the numerator we get \[(yx-y+xy+x) = \frac{xy+yx+x-y}{xy} = \frac{2xy}{xy}\]
5Step 5: Final Simplification
In the fraction \(\frac{2xy}{xy}\), 'xy' in the numerator and the denominator cancel each out leaving the final simplified result.
Other exercises in this chapter
Problem 79
Describe two similarities between the following problems: $$ \frac{3}{8}+\frac{1}{8} \text { and } \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1} $$
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Simplify each rational expression. $$\frac{9-y^{2}}{y^{2}-3(2 y-3)}$$
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In dividing polynomials $$2\(\frac{P}{Q} \div \frac{R}{S}$$ why is it necessary to state that polynomial \)R\( is not equal to \)0 ?$
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Solve each rational equation. $$\left(\frac{x+1}{x+7}\right)^{2} \div\left(\frac{x+1}{x+7}\right)^{4}=0$$
View solution