Solve x+1/x-1=2x-5/2x-7

$$\frac { x + 1 } { x - 1 } = \frac { 2 x - 5 } { 2 x - 7 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 1,\frac{7}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(2x-7\right), the least common multiple of x-1,2x-7.

$$\left(2x-7\right)\left(x+1\right)=\left(x-1\right)\left(2x-5\right)$$

Use the distributive property to multiply 2x-7 by x+1 and combine like terms.

$$2x^{2}-5x-7=\left(x-1\right)\left(2x-5\right)$$

Use the distributive property to multiply x-1 by 2x-5 and combine like terms.

$$2x^{2}-5x-7=2x^{2}-7x+5$$

Subtract 2x^{2} from both sides.

$$2x^{2}-5x-7-2x^{2}=-7x+5$$

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

$$-5x-7=-7x+5$$

Add 7x to both sides.

$$-5x-7+7x=5$$

Combine -5x and 7x to get 2x.

$$2x-7=5$$

Add 7 to both sides.

$$2x=5+7$$

Add 5 and 7 to get 12.

$$2x=12$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x=6$$