What is 5/x-(3x+2)/(x+1)+2/(x^2+x) ?

The solution to 5/x-(3x+2)/(x+1)+2/(x^2+x) is (-3x^2+3x+7)/(x(x+1))

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simplify 5/x-(3x+2)/(x+1)+2/(x^2+x)

simplify

\frac{5}{x} - \frac{3 x + 2}{x + 1} + \frac{2}{x ^{2} + x}

\frac{- 3 x ^{2} + 3 x + 7}{x ( x + 1 )}

Solution steps

\frac{5}{x} - \frac{3 x + 2}{x + 1} + \frac{2}{x ^{2} + x}

Least Common Multiplier of

x, x + 1, x^{2} + x : x (x + 1)

Adjust Fractions based on the LCM

= \frac{5 ( x + 1 )}{x ( x + 1 )} - \frac{( 3 x + 2 ) x}{x ( x + 1 )} + \frac{2}{x ( x + 1 )}

Apply the fraction rule:

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

= \frac{5 ( x + 1 ) - ( 3 x + 2 ) x + 2}{x ( x + 1 )}

Simplify

5 (x + 1) - (3 x + 2) x + 2 : - 3 x^{2} + 3 x + 7

= \frac{- 3 x ^{2} + 3 x + 7}{x ( x + 1 )}

8 \div \frac{1}{2}

(2 x^{2} + 7 x) + (- x^{2} + 10 x + 3)

3 f + 3 g

(- 8 - 9 i)^{2}

\frac{30}{40}

What is 5/x-(3x+2)/(x+1)+2/(x^2+x) ?
The solution to 5/x-(3x+2)/(x+1)+2/(x^2+x) is (-3x^2+3x+7)/(x(x+1))