Questions: Divide. (x-3)/(4x-4) ÷ (x+1)/(x^2+x-2)

Solution Steps

To divide rational expressions, multiply the first expression by the reciprocal of the second. Simplify the resulting expression by factoring and canceling common factors.

To divide the rational expressions, we multiply the first expression by the reciprocal of the second expression: \[ \frac{x-3}{4x-4} \div \frac{x+1}{x^2+x-2} = \frac{x-3}{4x-4} \times \frac{x^2+x-2}{x+1} \]

Multiply the numerators and the denominators: \[ \frac{(x-3)(x^2+x-2)}{(4x-4)(x+1)} \]

Factor the quadratic expression in the numerator and the linear expression in the denominator:

• \(x^2 + x - 2\) factors to \((x+2)(x-1)\).
• \(4x - 4\) factors to \(4(x-1)\).

The expression becomes: \[ \frac{(x-3)(x+2)(x-1)}{4(x-1)(x+1)} \]

Cancel the common factor \((x-1)\) from the numerator and the denominator: \[ \frac{(x-3)(x+2)}{4(x+1)} \]

Final Answer