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Add. \[ \frac{-5}{8 w^{2} y}+\frac{3}{4 w y^{2}} \] Simplify your answer as much as possible.

Ask by Hart Whittaker. in the United States
Mar 14,2025

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The simplified form is \(\frac{-5y + 6w}{8w^{2}y^{2}}\).

Solución

Calculate or simplify the expression \( \frac{-5}{8w^{2}y}+\frac{3}{4wy^{2}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{-5}{8w^{2}y}+\frac{3}{4wy^{2}}\) - step1: Rewrite the fraction: \(-\frac{5}{8w^{2}y}+\frac{3}{4wy^{2}}\) - step2: Reduce fractions to a common denominator: \(-\frac{5y}{8w^{2}y\times y}+\frac{3\times 2w}{4wy^{2}\times 2w}\) - step3: Multiply the numbers: \(-\frac{5y}{8w^{2}y\times y}+\frac{3\times 2w}{8wy^{2}w}\) - step4: Multiply the terms: \(-\frac{5y}{8w^{2}y^{2}}+\frac{3\times 2w}{8wy^{2}w}\) - step5: Multiply the terms: \(-\frac{5y}{8w^{2}y^{2}}+\frac{3\times 2w}{8w^{2}y^{2}}\) - step6: Transform the expression: \(\frac{-5y+3\times 2w}{8w^{2}y^{2}}\) - step7: Multiply the terms: \(\frac{-5y+6w}{8w^{2}y^{2}}\) The simplified form of the expression \(\frac{-5}{8w^{2}y}+\frac{3}{4wy^{2}}\) is \(\frac{-5y+6w}{8w^{2}y^{2}}\).

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The Deep Dive

To add the fractions, we first need to find a common denominator. The least common multiple of \(8wy^2\) and \(4wy^2\) is \(8wy^2\). Now we can rewrite each fraction with the common denominator: \[ \frac{-5}{8wy} + \frac{3 \cdot 2}{4wy^2 \cdot 2} = \frac{-5}{8wy} + \frac{6}{8wy^2} \] We need to convert \(\frac{-5}{8wy}\) to have the common denominator \(8wy^2\): \[ \frac{-5 \cdot y}{8wy^2} = \frac{-5y}{8wy^2} \] Now we can combine the two fractions: \[ \frac{-5y + 6}{8wy^2} \] So, the final simplified answer is: \[ \frac{-5y + 6}{8wy^2} \] This is the simplest form of the expression.

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