Problem 44
Question
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 y^{2}+4 y-4}{6 y^{2}-y-2}$$
Step-by-Step Solution
Verified Answer
The simplified form of the given rational expression \(\frac{3 y^{2}+4 y-4}{6 y^{2}-y-2}\) is \(\frac{(3y-2)}{(2y-1)}\).
1Step 1: 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 \((2y - 1)(3y + 2)\).
2Step 2: 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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Problem 44
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