What is (2x)/(3x^2+11x+6)+(x+1)/(x^2-9)+1/(3x+2) ?

The solution to (2x)/(3x^2+11x+6)+(x+1)/(x^2-9)+1/(3x+2) is (6x^2-x-7)/((x+3)(x-3)(3x+2))

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simplify (2x)/(3x^2+11x+6)+(x+1)/(x^2-9)+1/(3x+2)

simplify

\frac{2 x}{3 x ^{2} + 11 x + 6} + \frac{x + 1}{x ^{2} - 9} + \frac{1}{3 x + 2}

\frac{6 x ^{2} - x - 7}{( x + 3 ) ( x - 3 ) ( 3 x + 2 )}

Solution steps

\frac{2 x}{3 x ^{2} + 11 x + 6} + \frac{x + 1}{x ^{2} - 9} + \frac{1}{3 x + 2}

Least Common Multiplier of

3 x^{2} + 11 x + 6, x^{2} - 9, 3 x + 2 : (x + 3) (x - 3) (3 x + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 x (x - 3) + (x + 1) (3 x + 2) + (x + 3) (x - 3) : 6 x^{2} - x - 7

= \frac{6 x ^{2} - x - 7}{( x + 3 ) ( x - 3 ) ( 3 x + 2 )}

(2 x^{2} - 3 y)^{3}

2 x^{3} - 5 x^{2} - 4 x + 10

\frac{- 4 x ^{8} y ^{4}}{12 x ^{2} y}

\frac{3}{4} + \frac{2}{3} + \frac{1}{2}

What is (2x)/(3x^2+11x+6)+(x+1)/(x^2-9)+1/(3x+2) ?
The solution to (2x)/(3x^2+11x+6)+(x+1)/(x^2-9)+1/(3x+2) is (6x^2-x-7)/((x+3)(x-3)(3x+2))