What is (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40) ?

The solution to (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40) is -x+4

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simplify (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40)

simplify

\frac{x ^{2} - 16}{9 - x} \cdot \frac{x ^{2} + x - 90}{x ^{2} + 14 x + 40}

- x + 4

Solution steps

\frac{x ^{2} - 16}{9 - x} \cdot \frac{x ^{2} + x - 90}{x ^{2} + 14 x + 40}

Cancel

\frac{x ^{2} + x - 90}{x ^{2} + 14 x + 40} : \frac{x - 9}{x + 4}

= \frac{x ^{2} - 16}{9 - x} \cdot \frac{x - 9}{x + 4}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( x ^{2} - 16 ) ( x - 9 )}{( 9 - x ) ( x + 4 )}

9 - x = - (x - 9)

= \frac{( x ^{2} - 16 ) ( x - 9 )}{- ( x - 9 ) ( x + 4 )}

Cancel the common factor:

x - 9

= \frac{x ^{2} - 16}{- ( x + 4 )}

Factor

x^{2} - 16 : (x + 4) (x - 4)

= \frac{( x + 4 ) ( x - 4 )}{- ( x + 4 )}

Cancel the common factor:

x + 4

= \frac{x - 4}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (x - 4)

Apply the distributive law:

- (a - b) = - a + b

- (x - 4) = - x + 4

= - x + 4

(3 x - 2) (x + 5)

\frac{150}{1000}

2 x^{2} - 10 x - 28

2.5 \times 2.5

\frac{6}{3}

What is (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40) ?
The solution to (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40) is -x+4