What is (2x^2-162)/(2x^2-8x-90)*(x-7)/(x^5+2x^4-63x^3) ?

The solution to (2x^2-162)/(2x^2-8x-90)*(x-7)/(x^5+2x^4-63x^3) is 1/((x+5)x^3)

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simplify (2x^2-162)/(2x^2-8x-90)*(x-7)/(x^5+2x^4-63x^3)

simplify

\frac{2 x ^{2} - 162}{2 x ^{2} - 8 x - 90} \cdot \frac{x - 7}{x ^{5} + 2 x ^{4} - 63 x ^{3}}

\frac{1}{( x + 5 ) x ^{3}}

Solution steps

\frac{2 x ^{2} - 162}{2 x ^{2} - 8 x - 90} \cdot \frac{x - 7}{x ^{5} + 2 x ^{4} - 63 x ^{3}}

Cancel

\frac{2 x ^{2} - 162}{2 x ^{2} - 8 x - 90} : \frac{x + 9}{x + 5}

= \frac{x + 9}{x + 5} \cdot \frac{x - 7}{x ^{5} + 2 x ^{4} - 63 x ^{3}}

Cancel

\frac{x - 7}{x ^{5} + 2 x ^{4} - 63 x ^{3}} : \frac{1}{x ^{3} ( x + 9 )}

= \frac{x + 9}{x + 5} \cdot \frac{1}{x ^{3} ( x + 9 )}

Apply the fraction rule:

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

= \frac{( x + 9 ) \cdot 1}{( x + 5 ) x ^{3} ( x + 9 )}

Apply rule:

a \cdot 1 = a

(x + 9) \cdot 1 = (x + 9)

= \frac{x + 9}{( x + 5 ) x ^{3} ( x + 9 )}

Cancel the common factor:

x + 9

= \frac{1}{( x + 5 ) x ^{3}}

- 3 x^{2} + 45 x - 78

(- 5 - 4 i) (- 5 + 4 i)

10 x + 40

- 4^{2} + 3^{2}

(3 x^{2} + 2 x + 1) - (x^{2} - 3 x + 4)

What is (2x^2-162)/(2x^2-8x-90)*(x-7)/(x^5+2x^4-63x^3) ?
The solution to (2x^2-162)/(2x^2-8x-90)*(x-7)/(x^5+2x^4-63x^3) is 1/((x+5)x^3)