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Chapter 7: Problem 41

Add or subtract as indicated. Simplify the result, if possible. $$\frac{5 y}{y^{2}-9}-\frac{4}{y+3}$$

Short Answer

Expert verified
The result is \(\frac{y + 12}{(y+3)(y-3)}\)

Step by step solution

01

Identify the denominators

The denominators of the fractions are \(y^{2}-9\) and \(y+3\), respectively. They are not the same, so we need to find a common denominator to make subtraction possible.
02

Find common denominator

The expression \(y^{2}-9\) can be factorized to \((y+3)(y-3)\), since it's a difference of two squares. Therefore, the common denominator of the two fractions is \((y+3)(y-3)\).
03

Transform the fractions

To make the denominators the same we multiply the second fraction by \((y-3)/(y-3)\) which gives:\[\frac{5 y}{(y+3)(y-3)}- \frac{4(y-3)}{(y+3)(y-3)}\]
04

Subtract the fractions

Now that the denominators are the same, subtract the fractions:\[\frac{5 y - 4(y-3)}{(y+3)(y-3)}\]
05

Simplify the result

Simplify the numerator of the fraction:\[\frac{5 y - 4y + 12}{(y+3)(y-3)}=\frac{y + 12}{(y+3)(y-3)}\]

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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?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used \(\frac{a}{d}=\frac{b}{e}\) to show that corresponding sides of similar triangles are proportional, but I could also use \(\frac{a}{b}=\frac{d}{e}\) or \(\frac{d}{a}=\frac{e}{b}\)

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

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

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y}{y-4}-\frac{4}{4-y}$$
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