**Dividing Rational Expressions Step-by-Step Solution**This guide will walk you through the steps necessary to divide the rational expressions provided:Given:\[ \frac{x^2 - x - 42}{2x^2 + 4x} \div \frac{x - 7}{x + 2} \]Step 1: Change Division to MultiplicationRewrite the expression:\[ \frac{x^2 - x - 42}{2x^2 + 4x} \times \frac{x + 2}{x - 7} \]Step 2: Factorize the Numerator and DenominatorFactor each part of the expression.The numerator \(x^2 - x - 42\) factors to \((x - 7)(x + 6)\).The denominator \(2x^2 + 4x\) factors to \(2x(x + 2)\).Thus, the expression becomes:\[ \frac{(x - 7)(x + 6)}{2x(x + 2)} \times \frac{x + 2}{x - 7} \]Step 3: Combine and Simplify the ExpressionCombine the factored expressions:\[ \frac{(x - 7)(x + 6)(x + 2)}{2x(x + 2)(x - 7)} \]Step 4: Cancel Common FactorsCancel out the common factors in the numerator and denominator:- Cancel \((x + 2)\) from the numerator and denominator.- Cancel \((x - 7)\) from the numerator and denominator.The simplified expression is:\[ \frac{x + 6}{2x} \]Step 5: Final AnswerThus, the completely simplified form of the expression is represented as:\[ \frac{x + 6}{2x} \]

Name: **Dividing Rational Expressions Step-by-Step Solution**This guide wil
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: **Dividing Rational Expressions Step-by-Step Solution**This guide will walk you through the steps necessary to divide the rational expressions provided:Given:\[ \frac{x^2 - x - 42}{2x^2 + 4x} \div \frac{x - 7}{x + 2} \]Step 1: Change Division to Mul