What is (x^3+15x^2+54x)/(2x^4+6x^3-108x^2)*(6x^2-42x+36)/(x^2+5x-6) ?

The solution to (x^3+15x^2+54x)/(2x^4+6x^3-108x^2)*(6x^2-42x+36)/(x^2+5x-6) is 3/x

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simplify (x^3+15x^2+54x)/(2x^4+6x^3-108x^2)*(6x^2-42x+36)/(x^2+5x-6)

simplify

\frac{x ^{3} + 15 x ^{2} + 54 x}{2 x ^{4} + 6 x ^{3} - 108 x ^{2}} \cdot \frac{6 x ^{2} - 42 x + 36}{x ^{2} + 5 x - 6}

\frac{3}{x}

Solution steps

\frac{x ^{3} + 15 x ^{2} + 54 x}{2 x ^{4} + 6 x ^{3} - 108 x ^{2}} \cdot \frac{6 x ^{2} - 42 x + 36}{x ^{2} + 5 x - 6}

Cancel

\frac{x ^{3} + 15 x ^{2} + 54 x}{2 x ^{4} + 6 x ^{3} - 108 x ^{2}} : \frac{x + 6}{2 x ( x - 6 )}

= \frac{x + 6}{2 x ( x - 6 )} \cdot \frac{6 x ^{2} - 42 x + 36}{x ^{2} + 5 x - 6}

Cancel

\frac{6 x ^{2} - 42 x + 36}{x ^{2} + 5 x - 6} : \frac{6 ( x - 6 )}{x + 6}

= \frac{x + 6}{2 x ( x - 6 )} \cdot \frac{6 ( x - 6 )}{x + 6}

Cross-cancel common factor:

x + 6

= \frac{6 ( x - 6 )}{2 x ( x - 6 )}

Cancel the common factor:

x - 6

= \frac{6}{2 x}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 3}{2 x}

Cancel the common factor:

2

= \frac{3}{x}

\frac{- 5 t ^{5}}{( 5 t ^{- 5} ) ^{2}}

e^{i}

lo g_{a} (a^{3})

(2 + 4 x)^{2}

\frac{8}{15}

What is (x^3+15x^2+54x)/(2x^4+6x^3-108x^2)*(6x^2-42x+36)/(x^2+5x-6) ?
The solution to (x^3+15x^2+54x)/(2x^4+6x^3-108x^2)*(6x^2-42x+36)/(x^2+5x-6) is 3/x