How do I simplify $\frac{x^{2} - 5 x + 6}{x^{2} - 4} \cdot \frac{x^{2} + 3 x + 2}{x^{2} - 2 x - 3}$ $(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)$ ?

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How do I simplify $\frac{x^{2} - 5 x + 6}{x^{2} - 4} \cdot \frac{x^{2} + 3 x + 2}{x^{2} - 2 x - 3}$ $(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)$ ?

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Answer 1 · 2015-08-09T06:14:03

The answer to the problem is 1.

Explanation:

Factorize both denominator and Numerator.
= $\frac{x^{2} - 2 x - 3 x + 6}{(x + 2) (x - 2)}$ $(x^2 - 2x -3x +6)/((x + 2) (x - 2))$ . $\frac{x^{2} + x + 2 x + 2}{x^{2} - 3 x + x - 3}$ $(x^2 + x + 2x +2)/(x^2 - 3x + x -3)$

= $\frac{x (x - 2) - 3 (x - 2)}{(x + 2) (x - 2)}$ $(x(x - 2) -3( x - 2))/((x + 2) (x - 2))$ . $\frac{x (x + 1) + 2 (x + 1)}{x (x - 3) + 1 (x - 3)}$ $(x(x + 1) +2 (x + 1))/(x(x - 3) + 1 (x -3)$

= $\frac{(x - 2) (x - 3)}{(x + 2) (x - 2)}$ $((x - 2) ( x - 3))/((x + 2) (x - 2))$ . $\frac{(x + 1) (x + 2)}{(x - 3) (x + 1)}$ $((x + 1) (x + 2))/((x - 3) (x + 1)$ = 1

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How do I simplify $\frac{x^{2} - 5 x + 6}{x^{2} - 4} \cdot \frac{x^{2} + 3 x + 2}{x^{2} - 2 x - 3}$ $(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)$ ?

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How do I simplify x2−5x+6x2−4⋅x2+3x+2x2−2x−3(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)?

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How do I simplify $\frac{x^{2} - 5 x + 6}{x^{2} - 4} \cdot \frac{x^{2} + 3 x + 2}{x^{2} - 2 x - 3}$ $(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)$ ?