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Chapter 7: Problem 80

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

Short Answer

Expert verified
\(\frac{x^2+2x+y^2-2y}{xy}\)

Step by step solution

01

Determine common denominator

The denominators are \(y\) and \(x\). Their least common multiple (LCM) would be their product \(xy\).
02

Rewrite the fractions with a common denominator

The fractions can now be re-written as \(\frac{(x+2)x}{xy} + \(\frac{(y-2)y}{xy}\). By opening the brackets, we get \(\frac{x^2+2x}{xy} + \(\frac{y^2-2y}{xy}\).
03

Combine and simplify

The fractions have the common denominator, hence we add them to get \(\frac{x^2+2x+y^2-2y}{xy}\).

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Most popular questions from this chapter

If the ratio of the corresponding sides of two similar triangles is 1 to 1 ( \(\frac{1}{1}\) ), what must be true about the triangles?

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Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x}+9$$

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use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}+4 x+3}{x+2}-\frac{5 x+9}{x+2}=x-2, x \neq-2$$
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