What is 1/(2x^2+11x+15)+(6x+7)/(3x^2+7x-6)-(19)/(6x^2+11x-10) ?

The solution to 1/(2x^2+11x+15)+(6x+7)/(3x^2+7x-6)-(19)/(6x^2+11x-10) is 4/(2x+5)

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simplify 1/(2x^2+11x+15)+(6x+7)/(3x^2+7x-6)-(19)/(6x^2+11x-10)

simplify

\frac{1}{2 x ^{2} + 11 x + 15} + \frac{6 x + 7}{3 x ^{2} + 7 x - 6} - \frac{19}{6 x ^{2} + 11 x - 10}

\frac{4}{2 x + 5}

Solution steps

\frac{1}{2 x ^{2} + 11 x + 15} + \frac{6 x + 7}{3 x ^{2} + 7 x - 6} - \frac{19}{6 x ^{2} + 11 x - 10}

Least Common Multiplier of

2 x^{2} + 11 x + 15, 3 x^{2} + 7 x - 6, 6 x^{2} + 11 x - 10 : (x + 3) (2 x + 5) (3 x - 2)

Adjust Fractions based on the LCM

= \frac{3 x - 2}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )} + \frac{( 6 x + 7 ) ( 2 x + 5 )}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )} - \frac{19 ( x + 3 )}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )}

Apply the fraction rule:

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

= \frac{3 x - 2 + ( 6 x + 7 ) ( 2 x + 5 ) - 19 ( x + 3 )}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )}

Simplify

3 x - 2 + (6 x + 7) (2 x + 5) - 19 (x + 3) : 12 x^{2} + 28 x - 24

= \frac{12 x ^{2} + 28 x - 24}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )}

Cancel

\frac{12 x ^{2} + 28 x - 24}{( x + 3 ) ( 2 x + 5 ) ( 3 x - 2 )} : \frac{4}{2 x + 5}

= \frac{4}{2 x + 5}

(4 + 6 i) - (- 1 + 2 i)

\frac{1}{3 ( 125 ) ^{\frac{2}{3}}}

ln (1.03)

(4 z)^{3}

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

What is 1/(2x^2+11x+15)+(6x+7)/(3x^2+7x-6)-(19)/(6x^2+11x-10) ?
The solution to 1/(2x^2+11x+15)+(6x+7)/(3x^2+7x-6)-(19)/(6x^2+11x-10) is 4/(2x+5)