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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

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

Solution steps

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

Factor

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

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

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

Expand

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

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

\frac{( ( n ^{2} x ^{2} - 2 ) sin ( n x ) + 2 n x cos ( n x ) )}{n ^{3}}

\frac{- 5 z ^{2} - 10 i z + 6}{( z + i ) ^{3}} + 8

80 (e^{- t} - e^{- 2 t})

(5 + t + 5 - 5 t, (5 + t)^{2}) \cdot (1, - 1)

\frac{( 3 x - 2 ) ^{2}}{9}

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