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Chapter 7: Problem 44

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 y^{2}+4 y-4}{6 y^{2}-y-2}$$

Short Answer

Expert verified
The simplified form of the given rational expression \(\frac{3 y^{2}+4 y-4}{6 y^{2}-y-2}\) is \(\frac{(3y-2)}{(2y-1)}\).

Step by step solution

01

Factorizing the numerator and denominator

Factorize both the numerator \(3 y^{2}+4 y-4\) and the denominator \(6 y^{2}-y-2\). The numerator can be factorized to \((3y - 2)(y + 2)\), and the denominator can be factorized to \((2y - 1)(3y + 2)\).
02

Simplifying the rational expression

After factorization, look for common factors in the numerator and the denominator and cancel them out. In this case, when factored, the term \((3y + 2)\) exists in both the numerator and denominator, hence it can be canceled out. Therefore, the simplified form becomes \(\frac{(3y-2)}{(2y-1)}\).

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Most popular questions from this chapter

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 \(\frac{d}{a}=\frac{e}{b}\)

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