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

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

Solve for x

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

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.

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

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

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

Use the distributive property to multiply x-1 by 2.

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

Use the distributive property to multiply 2x-2 by x.

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

Subtract 2x^{2} from both sides.

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

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

$$-5x-7=-2x$$

Add 2x to both sides.

$$-5x-7+2x=0$$

Combine -5x and 2x to get -3x.

$$-3x-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$-3x=7$$

Divide both sides by -3.

$$x=\frac{7}{-3}$$

Fraction \frac{7}{-3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$x=-\frac{7}{3}$$