What is 3/(x^2+9x+18)-(7x)/(x+6) ?

The solution to 3/(x^2+9x+18)-(7x)/(x+6) is (3-7x^2-21x)/((x+3)(x+6))

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simplify 3/(x^2+9x+18)-(7x)/(x+6)

simplify

\frac{3}{x ^{2} + 9 x + 18} - \frac{7 x}{x + 6}

\frac{3 - 7 x ^{2} - 21 x}{( x + 3 ) ( x + 6 )}

Solution steps

\frac{3}{x ^{2} + 9 x + 18} - \frac{7 x}{x + 6}

Least Common Multiplier of

x^{2} + 9 x + 18, x + 6 : (x + 3) (x + 6)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 - 7 x (x + 3) : 3 - 7 x^{2} - 21 x

= \frac{3 - 7 x ^{2} - 21 x}{( x + 3 ) ( x + 6 )}

10 (- 4 x + 3 y) + (- 6) (- x - y + 2)

(7 x^{4} - 5 x^{5} + 4 x^{2} - 7) + (x^{3} - 3 x^{2} - 5 + x)

\frac{x ^{6} - y ^{6}}{x - y}

e^{\frac{1}{3} l n (x)}

(1 + 2 x)^{3}

What is 3/(x^2+9x+18)-(7x)/(x+6) ?
The solution to 3/(x^2+9x+18)-(7x)/(x+6) is (3-7x^2-21x)/((x+3)(x+6))