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Chapter 0: Problem 48

Add or subtract as indicated. $$\frac{x+3}{x-3}+\frac{x-3}{x+3}$$

Short Answer

Expert verified
The answer to the exercise is \[ \frac{2x^2 + 18}{(x-3)(x+3)} \]

Step by step solution

01

Find the common denominator

Here, the common denominator will be the product of the two individual denominators since they are not identical. Therefore, the common denominator is \((x - 3)(x + 3)\)
02

Rewrite fractions with common denominator

Re-write the two fractions with the common denominator, by multiplying each fraction by the excluded denominator of the other, so we get: \[ \frac{(x+3)(x+3)}{(x-3)(x+3)} + \frac{(x-3)(x-3)}{(x+3)(x-3)} \]
03

Simplify the numerators

We should apply the distributive property (FOIL Method) to simplify the numerators in the fractions we have: \[ \frac{x^2 + 6x + 9}{(x-3)(x+3)} + \frac{x^2 - 6x + 9}{(x+3)(x-3)} \]
04

Add the fractions

Now that the fractions have the same denominators we can add the numerators to get: \[ \frac{x^2 + 6x + 9 + x^2 - 6x + 9}{(x-3)(x+3)} \]
05

Simplify the fraction

Simplify by combining like terms in the numerator to get: \[ \frac{2x^2 + 18}{(x-3)(x+3} \]

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Most popular questions from this chapter

Explain how to factor the difference of two squares. Provide an example with your explanation.

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