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

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

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

factor

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

- \frac{1}{x - 1}

Solution steps

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

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

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

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

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

Expand

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

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

- x - 2 = - (x + 2)

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

Refine

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

Cancel the common factor:

x + 2

= - \frac{1}{x - 1}

11 + 3 (- 8 + 5 x) < 16 x - 5

- 2 (1 - 4 x) = 3 x + 8

28 - 7 x^{2}

6 x^{2} - 2 x - 2

\frac{a ^{2} + a}{2 a + 2}

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