What is 2/x+1/(x+1)-3 ?

The solution to 2/x+1/(x+1)-3 is (-3x^2+2)/(x(x+1))

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simplify 2/x+1/(x+1)-3

simplify

\frac{2}{x} + \frac{1}{x + 1} - 3

\frac{- 3 x ^{2} + 2}{x ( x + 1 )}

Solution steps

\frac{2}{x} + \frac{1}{x + 1} - 3

Join

\frac{2}{x} + \frac{1}{x + 1} : \frac{2 ( x + 1 ) + x}{x ( x + 1 )}

= \frac{2 ( x + 1 ) + x}{x ( x + 1 )} - 3

Apply the fraction rule:

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

= \frac{- 3 x ( x + 1 ) + 2 ( x + 1 ) + x}{x ( x + 1 )}

Simplify

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

= \frac{- 3 x ^{2} + 2}{x ( x + 1 )}

3 - 6 x

(2 x - 5) (3 x^{2} - 5 x - 4)

\frac{2 π}{\frac{4 π}{5}}

20 \times 5

lo g_{32} (\frac{1}{2})