What is (2x)/(x^2-3x-18)-5/(x^2+6x+9) ?

The solution to (2x)/(x^2-3x-18)-5/(x^2+6x+9) is (2x^2+x+30)/((x+3)^2(x-6))

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simplify (2x)/(x^2-3x-18)-5/(x^2+6x+9)

simplify

\frac{2 x}{x ^{2} - 3 x - 18} - \frac{5}{x ^{2} + 6 x + 9}

\frac{2 x ^{2} + x + 30}{( x + 3 ) ^{2} ( x - 6 )}

Solution steps

\frac{2 x}{x ^{2} - 3 x - 18} - \frac{5}{x ^{2} + 6 x + 9}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 x (x + 3) - 5 (x - 6) : 2 x^{2} + x + 30

= \frac{2 x ^{2} + x + 30}{( x + 3 ) ^{2} ( x - 6 )}

(x + y)^{13}

243 - 32 b^{5}

7 \cdot (- 1)

(5 x - 4) (5 x - 2)

\frac{2 x ^{4} - 10 x ^{3}}{6 x}

What is (2x)/(x^2-3x-18)-5/(x^2+6x+9) ?
The solution to (2x)/(x^2-3x-18)-5/(x^2+6x+9) is (2x^2+x+30)/((x+3)^2(x-6))