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Chapter 7: Problem 63

Divide as indicated. $$\frac{x y-y^{2}}{x^{2}+2 x+1} \div \frac{2 x^{2}+x y-3 y^{2}}{2 x^{2}+5 x y+3 y^{2}}$$

Short Answer

Expert verified
\(\frac{(x y-y^{2}) \cdot (2 x^{2}+5 x y+3 y^{2})}{(x^{2}+2 x+1) \cdot (2 x^{2}+x y-3 y^{2})}\)

Step by step solution

01

Reinterpret the division as a multiplication

Rewrite the problem as a multiplication: \(\frac{x y-y^{2}}{x^{2}+2 x+1} \cdot \frac{2 x^{2}+5 x y+3 y^{2}}{2 x^{2}+x y-3 y^{2}}\)
02

Multiply the numerators

Multiply the numerators of both fractions together: \( (x y-y^{2}) \cdot (2 x^{2}+5 x y+3 y^{2}) \)
03

Multiply the denominators

Multiply the denominators of both fractions together: \( (x^{2}+2 x+1) \cdot (2 x^{2}+x y-3 y^{2}) \)
04

Simplify if possible

Simplify the result if possible. In this case, no further simplification can be done.

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x}+4$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used \(\frac{a}{d}=\frac{b}{e}\) to show that corresponding sides of similar triangles are proportional, but I could also use \(\frac{a}{b}=\frac{d}{e}\) or \(\frac{d}{a}=\frac{e}{b}\)

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