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Chapter 7: Problem 103

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\)

Short Answer

Expert verified
The least common denominator is \( (x+10)(x-10)^{2} \)

Step by step solution

01

Factorizing \(x^{2}-100\)

This is a difference of squares. It can be factorized into \((x+10)(x-10)\)
02

Factorizing \(x^{2}-20 x+100\)

This is a perfect square trinomial, it can be factorized into \((x-10)^2\)
03

Getting the least common denominator

To get the least common denominator, get the product of the highest power of each factor from all the denominators. Here, the highest power of \((x+10)\) is 1 which is from \(x^{2}-100\), and the highest power of \((x-10)\) is 2 which is from \(x^{2}-20x+100\). So therefore, the least common denominator is \((x+10)(x-10)^{2}\)

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Most popular questions from this chapter

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{(y+1)(2 y-1)}{(y-2)(y-3)}+\frac{(y+2)(y-1)}{(y-2)(y-3)}-\frac{(y+5)(2 y+1)}{(3-y)(2-y)}$$

One pipe can fill a swimming pool in 2 hours, a second can fill the pool in 3 hours, and a third pipe can fill the pool in 4 hours. How many minutes, to the nearest minute, would it take to fill the pool with all three pipes operating?

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

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{y}{a x+b x-a y-b y}-\frac{x}{a x+b x-a y-b y}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}}$$
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