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

The solution to 1/(x^2+3x+2)-1/(x^2-2x-3) is -5/((x+1)(x+2)(x-3))

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simplify 1/(x^2+3x+2)-1/(x^2-2x-3)

simplify

\frac{1}{x ^{2} + 3 x + 2} - \frac{1}{x ^{2} - 2 x - 3}

- \frac{5}{( x + 1 ) ( x + 2 ) ( x - 3 )}

Solution steps

\frac{1}{x ^{2} + 3 x + 2} - \frac{1}{x ^{2} - 2 x - 3}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - 3 - (x + 2) : - 5

= \frac{- 5}{( x + 1 ) ( x + 2 ) ( x - 3 )}

Apply the fraction rule:

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

= - \frac{5}{( x + 1 ) ( x + 2 ) ( x - 3 )}

(2 - 3 i)^{- 5}

2 + (- 7)

\frac{x ^{2} - 25}{x ^{2} - 10 x + 25}

lo g_{4} (1 6^{2})

What is 1/(x^2+3x+2)-1/(x^2-2x-3) ?
The solution to 1/(x^2+3x+2)-1/(x^2-2x-3) is -5/((x+1)(x+2)(x-3))