What is (5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x) ?

The solution to (5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x) is 1/(3x)

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simplify (5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x)

simplify

\frac{5 x ^{2} - 40 x - 45}{15 x ^{2} - 195 x + 540} \cdot \frac{x ^{2} - 14 x + 40}{x ^{3} - 9 x ^{2} - 10 x}

\frac{1}{3 x}

Solution steps

\frac{5 x ^{2} - 40 x - 45}{15 x ^{2} - 195 x + 540} \cdot \frac{x ^{2} - 14 x + 40}{x ^{3} - 9 x ^{2} - 10 x}

Cancel

\frac{5 x ^{2} - 40 x - 45}{15 x ^{2} - 195 x + 540} : \frac{x + 1}{3 ( x - 4 )}

= \frac{x + 1}{3 ( x - 4 )} \cdot \frac{x ^{2} - 14 x + 40}{x ^{3} - 9 x ^{2} - 10 x}

Cancel

\frac{x ^{2} - 14 x + 40}{x ^{3} - 9 x ^{2} - 10 x} : \frac{x - 4}{x ( x + 1 )}

= \frac{x + 1}{3 ( x - 4 )} \cdot \frac{x - 4}{x ( x + 1 )}

Apply the fraction rule:

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

= \frac{( x + 1 ) ( x - 4 )}{3 ( x - 4 ) x ( x + 1 )}

Cancel the common factor:

x + 1

= \frac{x - 4}{3 ( x - 4 ) x}

Cancel the common factor:

x - 4

= \frac{1}{3 x}

121 - - 9 - 144 - - 16

(x - 2 y)^{7}

m (m - 1) (m - 2) (m - 3)

5 \cdot 1 0^{7}

\frac{42}{9}

What is (5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x) ?
The solution to (5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x) is 1/(3x)