Solve 4/2(x-2)=1/x+1+7/(x+1)(x-2)

$$\frac { 4 } { 2 ( x - 2 ) } = \frac { 1 } { x + 1 } + \frac { 7 } { ( x + 1 ) ( x - 2 ) }$$

Solve for x

$$x=3$$

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

$$\left(x+1\right)\times 4=2x-4+2\times 7$$

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

$$4x+4=2x-4+2\times 7$$

Multiply 2 and 7 to get 14.

$$4x+4=2x-4+14$$

Add -4 and 14 to get 10.

$$4x+4=2x+10$$

Subtract 2x from both sides.

$$4x+4-2x=10$$

Combine 4x and -2x to get 2x.

$$2x+4=10$$

Subtract 4 from both sides.

$$2x=10-4$$

Subtract 4 from 10 to get 6.

$$2x=6$$

Divide both sides by 2.

$$x=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x=3$$