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Chapter 7: Problem 54

Divide as indicated. $$\frac{3 y^{2}-12}{y^{2}+4 y+4} \div \frac{y^{3}-2 y^{2}}{y^{2}+2 y}$$

Short Answer

Expert verified
To get the final expression, it's necessary to cancel out common factors and simplify the fraction after carrying out the multiplications.

Step by step solution

01

Convert division to multiplication

Follow the algebraic rule of division, \((A \div B) = A \times (1/B)\), so the expression can be transformed to multiplication: \(\frac{3 y^{2}-12}{y^{2}+4 y+4} \times \frac{y^{2}+2 y}{y^{3}-2 y^{2}}\)
02

Multiply the numerators and denominators separately

Multiply the numerators and the denominators separately: \(\frac{(3 y^{2}-12) \times (y^{2}+2 y)}{(y^{2}+4 y+4) \times (y^{3}-2 y^{2})}\)
03

Simplify result

Expand the two multiplications separately, then simplify the fraction by canceling out common factors. This will lead to the final expression.

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Most popular questions from this chapter

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\text { Simplify: } \frac{(y+2) y-2 \cdot 4}{4 y(y+4)}$$

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denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x+3}{x^{2}-x-30}+\frac{x-2}{30+x-x^{2}}$$
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