Solve 4/x^2-1=3/x+1-4/3(x-1)

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

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 3\left(x-1\right)\left(x+1\right), the least common multiple of x^{2}-1,x+1,3\left(x-1\right).

$$3\times 4=\left(3x-3\right)\times 3-\left(x+1\right)\times 4$$

Multiply 3 and 4 to get 12.

$$12=\left(3x-3\right)\times 3-\left(x+1\right)\times 4$$

Use the distributive property to multiply 3x-3 by 3.

$$12=9x-9-\left(x+1\right)\times 4$$

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

$$12=9x-9-\left(4x+4\right)$$

To find the opposite of 4x+4, find the opposite of each term.

$$12=9x-9-4x-4$$

Combine 9x and -4x to get 5x.

$$12=5x-9-4$$

Subtract 4 from -9 to get -13.

$$12=5x-13$$

Swap sides so that all variable terms are on the left hand side.

$$5x-13=12$$

Add 13 to both sides.

$$5x=12+13$$

Add 12 and 13 to get 25.

$$5x=25$$

Divide both sides by 5.

$$x=\frac{25}{5}$$

Divide 25 by 5 to get 5.

$$x=5$$