What is expand 1/(x+1)-1/(x+2) ?

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

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expand 1/(x+1)-1/(x+2)

expand

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

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

Solution steps

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

Least Common Multiplier of

x + 1, x + 2 : (x + 1) (x + 2)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

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

Expand

x + 2 - (x + 1) : 1

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

\frac{x ^{3} - x ^{2}}{( x - 1 ) ^{2} + x ^{4}}

\frac{16 ( 16 + 2 x - x ^{2} )}{( 8 x - x ^{2} ) ^{6}}

- \frac{2 ( y - 3 )}{5}

\frac{f ( b ^{2} - a ^{2} )}{2}

cos (2 t) U (t - \frac{5 π}{2})

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