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Chapter 7: Problem 28

Multiply as indicated. $$\frac{2 y}{3 y-y^{2}} \cdot \frac{2 y^{2}-9 y+9}{8 y-12}$$

Short Answer

Expert verified
The solution to the multiplication of the fractions is \(\frac{y^2 - 3y}{6 (1-y) }\).

Step by step solution

01

Rewrite and Simplify the Problem

Rewrite the expression by factoring the numerator of the second fraction and the denominator of the first fraction. Expression can be rewritten as: \(\frac{2 y}{3 y(1-y)} \cdot \frac{(y-3)^2}{4(2 y-3)}\)
02

Cancel Out Common Factors

Identify and cancel out common factors in the numerators and denominators of the fractions. Hence, we get: \(\frac{2 y}{3 (1-y)} \cdot \frac{(y-3)}{4}\)
03

Perform the Multiplication

Multiply the numerators with each other and the denominators with each other to get the result: \( \frac{2 y \cdot (y-3)}{3 (1-y) \cdot 4 }\)
04

Simplify the Result

Simplify further to obtain the final answer: \(\frac{(2 y \cdot (y-3))}{12 (1-y) } = \frac{y^2 - 3y}{6 (1-y) } \)

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Most popular questions from this chapter

Use a proportion to solve each problem. Height is proportional to foot length. A person whose foot length is 10 inches is 67 inches tall. In 1951 , photos of large footprints were published. Some believed that these footprints were made by the "Abominable Snowman." Each footprint was 23 inches long. If indeed they belonged to the Abominable Snowman, how tall is the critter? (IMAGE CANNOT COPY)

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{6 b^{2}-10 b}{16 b^{2}-48 b+27}+\frac{7 b^{2}-20 b}{16 b^{2}-48 b+27}-\frac{6 b-3 b^{2}}{16 b^{2}-48 b+27}$$

If the ratio of the corresponding sides of two similar triangles is 1 to 1 ( \(\frac{1}{1}\) ), what must be true about the triangles?

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-1}-\frac{5}{1-x}$$
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