What is (x+1)/(x+1)-(4x)/(x-1)+4/(x^2-1) ?

The solution to (x+1)/(x+1)-(4x)/(x-1)+4/(x^2-1) is (-3x^2-4x+3)/((x+1)(x-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x+1)/(x+1)-(4x)/(x-1)+4/(x^2-1)

simplify

\frac{x + 1}{x + 1} - \frac{4 x}{x - 1} + \frac{4}{x ^{2} - 1}

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

Solution steps

\frac{x + 1}{x + 1} - \frac{4 x}{x - 1} + \frac{4}{x ^{2} - 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( x + 1 ) ( x - 1 )}{( x + 1 ) ( x - 1 )} - \frac{4 x ( x + 1 )}{( x + 1 ) ( x - 1 )} + \frac{4}{( x + 1 ) ( x - 1 )}

Apply the fraction rule:

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

= \frac{( x + 1 ) ( x - 1 ) - 4 x ( x + 1 ) + 4}{( x + 1 ) ( x - 1 )}

Simplify

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

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

x^{3} - 10 x^{2} + 24 x

- 5 x^{2} (6 x - 1)

(\frac{4}{5 + 1} + 1)^{2}

- 16 \cdot (- 2)

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

What is (x+1)/(x+1)-(4x)/(x-1)+4/(x^2-1) ?
The solution to (x+1)/(x+1)-(4x)/(x-1)+4/(x^2-1) is (-3x^2-4x+3)/((x+1)(x-1))