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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 2 to get 4.

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

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

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

Add 2 and 4 to get 6.

$$6+4x=5\left(x+1\right)$$

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

$$6+4x=5x+5$$

Subtract 5x from both sides.

$$6+4x-5x=5$$

Combine 4x and -5x to get -x.

$$6-x=5$$

Subtract 6 from both sides.

$$-x=5-6$$

Subtract 6 from 5 to get -1.

$$-x=-1$$

Multiply both sides by -1.

$$x=1$$