What is 2/((x-2))-6/(x^2)-x-2 ?

The solution to 2/((x-2))-6/(x^2)-x-2 is (-x^4+6x^2-6x+12)/(x^2(x-2))

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simplify 2/((x-2))-6/(x^2)-x-2

simplify

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

\frac{- x ^{4} + 6 x ^{2} - 6 x + 12}{x ^{2} ( x - 2 )}

Solution steps

\frac{2}{x - 2} - \frac{6}{x ^{2}} - x - 2

Join

\frac{2}{x - 2} - \frac{6}{x ^{2}} : \frac{2 x ^{2} - 6 ( x - 2 )}{x ^{2} ( x - 2 )}

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

Convert

x

to fraction

: \frac{x ^{3} ( x - 2 )}{x ^{2} ( x - 2 )}

Convert

2

to fraction

: \frac{2 x ^{2} ( x - 2 )}{x ^{2} ( x - 2 )}

= \frac{2 x ^{2} - 6 ( x - 2 )}{x ^{2} ( x - 2 )} - \frac{x ^{3} ( x - 2 )}{x ^{2} ( x - 2 )} - \frac{2 x ^{2} ( x - 2 )}{x ^{2} ( x - 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{2 x ^{2} - 6 ( x - 2 ) - x ^{3} ( x - 2 ) - 2 x ^{2} ( x - 2 )}{x ^{2} ( x - 2 )}

Simplify

2 x^{2} - 6 (x - 2) - x^{3} (x - 2) - 2 x^{2} (x - 2) : - x^{4} + 6 x^{2} - 6 x + 12

= \frac{- x ^{4} + 6 x ^{2} - 6 x + 12}{x ^{2} ( x - 2 )}

0.2 x - (0.4 x - 0.8 x)

8 x^{2} y^{2} - x^{5}

2 x - 22

(10 x + 0.1)^{2}

6 c^{3} \cdot a^{- 2}

What is 2/((x-2))-6/(x^2)-x-2 ?
The solution to 2/((x-2))-6/(x^2)-x-2 is (-x^4+6x^2-6x+12)/(x^2(x-2))