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

The solution to x/(x^2+3x+2)+3/(x+1) is (4x+6)/((x+1)(x+2))

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

simplify

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

\frac{4 x + 6}{( x + 1 ) ( x + 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + 3 (x + 2) : 4 x + 6

= \frac{4 x + 6}{( x + 1 ) ( x + 2 )}

\frac{5}{7 - 2}

lo g_{\frac{1}{3}} (4)

2 \times 6

\frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3 x + 6}{x ^{2} + 7 x + 10}

\frac{2}{5} \times \frac{1}{4}

What is x/(x^2+3x+2)+3/(x+1) ?
The solution to x/(x^2+3x+2)+3/(x+1) is (4x+6)/((x+1)(x+2))