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Chapter 7: Problem 44

Add or subtract as indicated. Simplify the result, if possible. $$\frac{5}{x+3}-\frac{2}{(x+3)^{2}}$$

Short Answer

Expert verified
The simplified result is \(\frac{5x+13}{(x+3)^{2}}\)

Step by step solution

01

Identify common denominator

Since the second denominator is the square of the first denominator, we can use \((x+3)^{2}\) as the common denominator.
02

Create equivalent fractions

To make the first fraction have \((x+3)^{2}\) as the denominator, multiply the numerator and denominator of the first fraction by \((x+3)\):\[\frac{5}{x+3} * \frac{x+3}{x+3} = \frac{5(x+3)}{(x+3)^{2}}\]This gives us two fractions with the same denominator:\[\frac{5(x+3)}{(x+3)^{2}}-\frac{2}{(x+3)^{2}}\]
03

Subtract fractions

Now that the two fractions have the same denominator, subtract the numerators:\[\frac{5(x+3)-2}{(x+3)^{2}}\]
04

Simplify the result

Expand the numerator, simplify and collect like terms:\[\frac{5x+15-2}{(x+3)^{2}} = \frac{5x+13}{(x+3)^{2}}\]

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Most popular questions from this chapter

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x^{2}-4 x+4}{3 x^{2}+7 x+2}-\frac{10 x+9}{3 x^{2}+7 x+2}\right) \div \frac{x-5}{x^{2}-4}$$

Subtract: \(\frac{13}{15}-\frac{8}{45}\) (Section 1.2, Example 9)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.. $$Find the missing polynomials: $\quad-\frac{3 x-12}{2 x}=\frac{3}{2}$$

What are similar triangles?

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}\right) \div \frac{x+2}{x^{2}-1}$$
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