Solve 1/x-5-4/x+1=2/x^2-4x-5

$$\frac { 1 } { x - 5 } - \frac { 4 } { x + 1 } = \frac { 2 } { x ^ { 2 } - 4 x - 5 }$$

Solve for x

$$x = \frac{19}{3} = 6\frac{1}{3} \approx 6.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+1\right), the least common multiple of x-5,x+1,x^{2}-4x-5.

$$x+1-\left(x-5\right)\times 4=2$$

Use the distributive property to multiply x-5 by 4.

$$x+1-\left(4x-20\right)=2$$

To find the opposite of 4x-20, find the opposite of each term.

$$x+1-4x+20=2$$

Combine x and -4x to get -3x.

$$-3x+1+20=2$$

Add 1 and 20 to get 21.

$$-3x+21=2$$

Subtract 21 from both sides.

$$-3x=2-21$$

Subtract 21 from 2 to get -19.

$$-3x=-19$$

Divide both sides by -3.

$$x=\frac{-19}{-3}$$

Fraction \frac{-19}{-3} can be simplified to \frac{19}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{19}{3}$$