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Chapter 0: Problem 19

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

Short Answer

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

Step by step solution

01

Factorize the polynomials

Rewrite all the polynomials in factored form: \( (x-3)(x-2)\) / \((x-3)(x+1)\) \cdot \((x-1)(x+1)\) / \((x-2)(x+2)\) .
02

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.
03

Write the final answer

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

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Most popular questions from this chapter

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Evaluate each expression without using a calculator. $$27^{\frac{1}{3}}$$

Find all integers b so that the trinomial can be factored. $$ x^{2}+4 x+b $$
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