Solve 0/x^2-1-6/x-1=5/x+1

$$\frac { 0 } { x ^ { 2 } - 1 } - \frac { 6 } { x - 1 } = \frac { 5 } { x + 1 }$$

Solve for x

$$x=-\frac{1}{11}\approx -0.090909091$$

Steps for Solving Linear Equation

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

$$0-\left(x+1\right)\times 6=\left(x-1\right)\times 5$$

Use the distributive property to multiply x+1 by 6.

$$0-\left(6x+6\right)=\left(x-1\right)\times 5$$

To find the opposite of 6x+6, find the opposite of each term.

$$0-6x-6=\left(x-1\right)\times 5$$

Subtract 6 from 0 to get -6.

$$-6-6x=\left(x-1\right)\times 5$$

Use the distributive property to multiply x-1 by 5.

$$-6-6x=5x-5$$

Subtract 5x from both sides.

$$-6-6x-5x=-5$$

Combine -6x and -5x to get -11x.

$$-6-11x=-5$$

Add 6 to both sides.

$$-11x=-5+6$$

Add -5 and 6 to get 1.

$$-11x=1$$

Divide both sides by -11.

$$x=\frac{1}{-11}$$

Fraction \frac{1}{-11} can be rewritten as -\frac{1}{11} by extracting the negative sign.

$$x=-\frac{1}{11}$$