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

$$x = \frac{23}{3} = 7\frac{2}{3} \approx 7.666666667$$

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 -23.

$$-3x=-23$$

Divide both sides by -3.

$$x=\frac{-23}{-3}$$

Fraction \frac{-23}{-3} can be simplified to \frac{23}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{23}{3}$$