What is (9-p^2)/(3-2p-p^2)*(p^2+p-2)/(p^2-p-6) ?

The solution to (9-p^2)/(3-2p-p^2)*(p^2+p-2)/(p^2-p-6) is 1

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simplify (9-p^2)/(3-2p-p^2)*(p^2+p-2)/(p^2-p-6)

simplify

\frac{9 - p ^{2}}{3 - 2 p - p ^{2}} \cdot \frac{p ^{2} + p - 2}{p ^{2} - p - 6}

1

Solution steps

\frac{9 - p ^{2}}{3 - 2 p - p ^{2}} \cdot \frac{p ^{2} + p - 2}{p ^{2} - p - 6}

Cancel

\frac{9 - p ^{2}}{3 - 2 p - p ^{2}} : - \frac{3 - p}{p - 1}

= - \frac{3 - p}{p - 1} \cdot \frac{p ^{2} + p - 2}{p ^{2} - p - 6}

Cancel

\frac{p ^{2} + p - 2}{p ^{2} - p - 6} : \frac{p - 1}{p - 3}

= - \frac{3 - p}{p - 1} \cdot \frac{p - 1}{p - 3}

Cross-cancel common factor:

p - 1

= - \frac{3 - p}{p - 3}

Cancel

\frac{3 - p}{p - 3} : - 1

= - (- 1)

Apply rule:

- (- a) = a

- (- 1) = 1

= 1

(3 x + 9) (2 x + 8)

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What is (9-p^2)/(3-2p-p^2)*(p^2+p-2)/(p^2-p-6) ?
The solution to (9-p^2)/(3-2p-p^2)*(p^2+p-2)/(p^2-p-6) is 1