What is 1/(x^2+3x-18)-4/(7x^2-11x-30) ?

The solution to 1/(x^2+3x-18)-4/(7x^2-11x-30) is (3x-14)/((x-3)(x+6)(7x+10))

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simplify 1/(x^2+3x-18)-4/(7x^2-11x-30)

simplify

\frac{1}{x ^{2} + 3 x - 18} - \frac{4}{7 x ^{2} - 11 x - 30}

\frac{3 x - 14}{( x - 3 ) ( x + 6 ) ( 7 x + 10 )}

Solution steps

\frac{1}{x ^{2} + 3 x - 18} - \frac{4}{7 x ^{2} - 11 x - 30}

Least Common Multiplier of

x^{2} + 3 x - 18, 7 x^{2} - 11 x - 30 : (x - 3) (x + 6) (7 x + 10)

Adjust Fractions based on the LCM

= \frac{7 x + 10}{( x - 3 ) ( x + 6 ) ( 7 x + 10 )} - \frac{4 ( x + 6 )}{( x - 3 ) ( x + 6 ) ( 7 x + 10 )}

Apply the fraction rule:

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

= \frac{7 x + 10 - 4 ( x + 6 )}{( x - 3 ) ( x + 6 ) ( 7 x + 10 )}

Simplify

7 x + 10 - 4 (x + 6) : 3 x - 14

= \frac{3 x - 14}{( x - 3 ) ( x + 6 ) ( 7 x + 10 )}

\frac{23}{10}

\frac{36}{24}

(6 + 10 i) - (1 + 7 i)

(3 x + 2) (2 x - 1)

1 0^{3} - 6 + 2 [9 x - 10 - (3 - x)] - 9^{2}

What is 1/(x^2+3x-18)-4/(7x^2-11x-30) ?
The solution to 1/(x^2+3x-18)-4/(7x^2-11x-30) is (3x-14)/((x-3)(x+6)(7x+10))