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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 is \(\frac{2x^2+18}{x^2-9}\)

Step by step solution

01

Multiply the Fractions

Multiply each fraction by the other fraction's denominator over itself. This gives: \(\frac{(x+3)(x+3)}{(x-3)(x+3)}+\frac{(x-3)(x-3)}{(x+3)(x-3)}\). This makes the denominators the same, allowing us to add the fractions in the next step.
02

Simplifying the Fractions and Addition

Now we simplify each fraction and add them, like so: \(\frac{x^2+6x+9}{x^2-9}+\frac{x^2-6x+9}{x^2-9}=\frac{x^2+6x+9+x^2-6x+9}{x^2-9}\). Notice that \(+6x\) and \(-6x\) cancel each other.
03

Final Simplification

Combine like-terms in the numerator to find the final result: \(\frac{2x^2+18}{x^2-9}\).

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Most popular questions from this chapter

Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$

Simplify using properties of exponents. $$\frac{\left(2 y^{\frac{1}{5}}\right)^{4}}{y^{\frac{3}{10}}}$$

Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$

Find all integers b so that the trinomial can be factored. $$ x^{2}+b x+15 $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$5^{2} \cdot 5^{-2}>2^{5} \cdot 2^{-5}$$
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