QuestionDecember 25, 2025

b) (-4)/(3-2z)+(4z+18)/(9-4z^2)

b) (-4)/(3-2z)+(4z+18)/(9-4z^2)
b) (-4)/(3-2z)+(4z+18)/(9-4z^2)

Solution
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Answer

\frac{6 - 4z}{(3-2z)(3+2z)} Explanation 1. Find common denominator 9 - 4z^2 = (3 - 2z)(3 + 2z) is the common denominator. 2. Rewrite fractions with common denominator \frac{-4}{3-2z} = \frac{-4(3+2z)}{(3-2z)(3+2z)}, \frac{4z+18}{9-4z^2} stays as is. 3. Combine numerators = \frac{-4(3+2z) + (4z+18)}{(3-2z)(3+2z)} 4. Simplify numerator -12 - 8z + 4z + 18 = (6 - 4z)

Explanation

1. Find common denominator<br /> $9 - 4z^2 = (3 - 2z)(3 + 2z)$ is the common denominator.<br />2. Rewrite fractions with common denominator<br /> $\frac{-4}{3-2z} = \frac{-4(3+2z)}{(3-2z)(3+2z)}$, $\frac{4z+18}{9-4z^2}$ stays as is.<br />3. Combine numerators<br /> $= \frac{-4(3+2z) + (4z+18)}{(3-2z)(3+2z)}$<br />4. Simplify numerator<br /> $-12 - 8z + 4z + 18 = (6 - 4z)$
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