Solve x/x+1-3/x-1=1

$$\frac{ x }{ x+1 } - \frac{ 3 }{ x-1 } = 1$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

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), the least common multiple of x+1,x-1.

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

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

$$x^{2}-x-\left(x+1\right)\times 3=\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply x+1 by 3.

$$x^{2}-x-\left(3x+3\right)=\left(x-1\right)\left(x+1\right)$$

To find the opposite of 3x+3, find the opposite of each term.

$$x^{2}-x-3x-3=\left(x-1\right)\left(x+1\right)$$

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

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}-4x-3=x^{2}-1$$

Subtract x^{2} from both sides.

$$x^{2}-4x-3-x^{2}=-1$$

Combine x^{2} and -x^{2} to get 0.

$$-4x-3=-1$$

Add 3 to both sides.

$$-4x=-1+3$$

Add -1 and 3 to get 2.

$$-4x=2$$

Divide both sides by -4.

$$x=\frac{2}{-4}$$

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{2}$$