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Simplify: \( \frac{(x-3)(x+1)}{(x+5)} \cdot \frac{7(x+5)}{(x+7)(x-3)} \) What would be left in the numerator (top) use PARENTHESES if needed and NO SPACES: What would be left in the denominator (bottom) use PARENTHESES if needed and NO SPACES

Ask by Murphy Morgan. in the United States
Feb 05,2025

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Numerator: 7x+7 Denominator: x+7

Solución

Calculate or simplify the expression \( \frac{(x-3)(x+1)}{(x+5)} \cdot \frac{7(x+5)}{(x+7)(x-3)} \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x-3\right)\left(x+1\right)}{\left(x+5\right)}\times \frac{7\left(x+5\right)}{\left(x+7\right)\left(x-3\right)}\) - step1: Remove the parentheses: \(\frac{\left(x-3\right)\left(x+1\right)}{x+5}\times \frac{7\left(x+5\right)}{\left(x+7\right)\left(x-3\right)}\) - step2: Reduce the fraction: \(\left(x+1\right)\times \frac{7}{x+7}\) - step3: Multiply the terms: \(\frac{\left(x+1\right)\times 7}{x+7}\) - step4: Multiply the terms: \(\frac{7\left(x+1\right)}{x+7}\) - step5: Simplify: \(\frac{7x+7}{x+7}\) The simplified expression is \( \frac{7x+7}{x+7} \). The numerator (top) would be \( 7x+7 \) and the denominator (bottom) would be \( x+7 \).

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The expression simplifies as follows: \[ \frac{(x-3)(x+1)}{(x+5)} \cdot \frac{7(x+5)}{(x+7)(x-3)} \] First, we can cancel the common factors in the numerator and the denominator. The \( (x-3) \) appears in both the numerator and the denominator, and the \( (x+5) \) also cancels out. So we are left with: Numerator: \( 7(x+1) \) Denominator: \( (x+7) \) Therefore: Numerator: \( 7(x+1) \) Denominator: \( (x+7) \)

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