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

The solution to (3x^2+2x+2)/(x^3+1)+2/(x+1) is (5x^2+4)/((x+1)(x^2-x+1))

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

simplify

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

\frac{5 x ^{2} + 4}{( x + 1 ) ( x ^{2} - x + 1 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 x^{2} + 2 x + 2 + 2 (x^{2} - x + 1) : 5 x^{2} + 4

= \frac{5 x ^{2} + 4}{( x + 1 ) ( x ^{2} - x + 1 )}

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

\frac{\frac{4}{3}}{3}

11 \frac{3}{5} + 9 \frac{1}{4}

lo g_{- 1} (x)

What is (3x^2+2x+2)/(x^3+1)+2/(x+1) ?
The solution to (3x^2+2x+2)/(x^3+1)+2/(x+1) is (5x^2+4)/((x+1)(x^2-x+1))