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Chapter 0: Problem 32

Multiply or divide as indicated. $$\frac{x^{3}-25 x}{4 x^{2}} \cdot \frac{2 x^{2}-2}{x^{2}-6 x+5} \div \frac{x^{2}+5 x}{7 x+7}$$

Short Answer

Expert verified
The simplified form of the given expression is \( \frac{7 * (x+1)}{2} \)

Step by step solution

01

Break down the expression

Given that we need to perform both multiplication and division operations, the expression can be rewritten as: \(\frac{\frac{(x^{3}-25 x)}{(4x^{2})} * \frac{(2 x^{2}-2)}{(x^{2}-6 x+5)}}{\frac{(x^{2}+5x)}{(7x+7)}}\)
02

Simplify individual expressions

Each part of the fraction can be simplified by factoring, if possible. As a result, the equation becomes: \(\frac{(x(x-5)(x+5)) * 2(x-1)}{(4x^{2}) * (x-5)(x-1)} * \frac{1}{\frac{x(x+5)}{7(x+1)}}\)
03

Simplify complex fraction

We can now reduce this complex fraction by cancelling common terms across numerators and denominators. After simplification, the equation becomes: \( \frac{2 * (x+5)}{4x} * \frac{7(x+1)}{x}\)
04

Simplify further and solve

Continue to simplify above fraction by cancelling common terms across numerators and denominators again. After simplification, the equation becomes: \( \frac{7 * (x+1)}{2}\)

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Most popular questions from this chapter

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