Solve 6/x^2-1=4/(x-1)^2

$$\frac { 6 } { x ^ { 2 } - 1 } = \frac { 4 } { ( x - 1 ) ^ { 2 } }$$

Solve for x

$$x=5$$

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)^{2}, the least common multiple of x^{2}-1,\left(x-1\right)^{2}.

$$\left(x-1\right)\times 6=\left(x+1\right)\times 4$$

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

$$6x-6=\left(x+1\right)\times 4$$

Use the distributive property to multiply x+1 by 4.

$$6x-6=4x+4$$

Subtract 4x from both sides.

$$6x-6-4x=4$$

Combine 6x and -4x to get 2x.

$$2x-6=4$$

Add 6 to both sides.

$$2x=4+6$$

Add 4 and 6 to get 10.

$$2x=10$$

Divide both sides by 2.

$$x=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$x=5$$