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

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

Solve for x

$$x = \frac{13}{9} = 1\frac{4}{9} \approx 1.444444444$$

Steps for Solving Linear Equation

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

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

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

$$2x-4+\left(x-1\right)\times 5=\left(2-x\right)\times 2$$

Use the distributive property to multiply x-1 by 5.

$$2x-4+5x-5=\left(2-x\right)\times 2$$

Combine 2x and 5x to get 7x.

$$7x-4-5=\left(2-x\right)\times 2$$

Subtract 5 from -4 to get -9.

$$7x-9=\left(2-x\right)\times 2$$

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

$$7x-9=4-2x$$

Add 2x to both sides.

$$7x-9+2x=4$$

Combine 7x and 2x to get 9x.

$$9x-9=4$$

Add 9 to both sides.

$$9x=4+9$$

Add 4 and 9 to get 13.

$$9x=13$$

Divide both sides by 9.

$$x=\frac{13}{9}$$