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

The solution to x/(x^2+5x+6)-2/(x^2+3x+2) is (x-3)/((x+3)(x+1))

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x^{2} + 5 x + 6, x^{2} + 3 x + 2 : (x + 2) (x + 3) (x + 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x (x + 1) - 2 (x + 3) : x^{2} - x - 6

= \frac{x ^{2} - x - 6}{( x + 2 ) ( x + 3 ) ( x + 1 )}

Cancel

\frac{x ^{2} - x - 6}{( x + 2 ) ( x + 3 ) ( x + 1 )} : \frac{x - 3}{( x + 3 ) ( x + 1 )}

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

\frac{1 + 2 i}{1 - 3 i}

- 5 - - 44

\frac{42}{63}

sec (x) csc (x)

50 b^{4}

What is x/(x^2+5x+6)-2/(x^2+3x+2) ?
The solution to x/(x^2+5x+6)-2/(x^2+3x+2) is (x-3)/((x+3)(x+1))