Problem 19 - College Algebra

Question

Multiply or divide as indicated. $$\frac{x^{2}-5 x+6}{x^{2}-2 x-3} \cdot \frac{x^{2}-1}{x^{2}-4}$$

Step-by-Step Solution

Answer

The simplified expression is \((x+1)\) / \((x+2)\).

Step 1: Factorize the polynomials

Rewrite all the polynomials in factored form: \( (x-3)(x-2)\) / \((x-3)(x+1)\) \cdot \((x-1)(x+1)\) / \((x-2)(x+2)\) .

Step 2: Cancel common factors

Cancel out the common factors: (x-2) is common between the numerator and the denominator, and (x-3) is also common between the numerator and the denominator, so we eliminate these terms from both. This reduces the expression to: \((x+1)\) / \((x+2)\).\n This cannot be further simplified.

Step 3: Write the final answer

The final answer after cancellation is \((x+1)\) / \((x+2)\).