Solve x+1/x+2=2/3+1/2

$$\frac { x + 1 } { x + 2 } = \frac { 2 } { 3 } + \frac { 1 } { 2 }$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+2\right), the least common multiple of x+2,3,2.

$$6\left(x+1\right)=6\left(x+2\right)\times \frac{2}{3}+6\left(x+2\right)\times \frac{1}{2}$$

Use the distributive property to multiply 6 by x+1.

$$6x+6=6\left(x+2\right)\times \frac{2}{3}+6\left(x+2\right)\times \frac{1}{2}$$

Multiply 6 and \frac{2}{3} to get 4.

$$6x+6=4\left(x+2\right)+6\left(x+2\right)\times \frac{1}{2}$$

Use the distributive property to multiply 4 by x+2.

$$6x+6=4x+8+6\left(x+2\right)\times \frac{1}{2}$$

Multiply 6 and \frac{1}{2} to get 3.

$$6x+6=4x+8+3\left(x+2\right)$$

Use the distributive property to multiply 3 by x+2.

$$6x+6=4x+8+3x+6$$

Combine 4x and 3x to get 7x.

$$6x+6=7x+8+6$$

Add 8 and 6 to get 14.

$$6x+6=7x+14$$

Subtract 7x from both sides.

$$6x+6-7x=14$$

Combine 6x and -7x to get -x.

$$-x+6=14$$

Subtract 6 from both sides.

$$-x=14-6$$

Subtract 6 from 14 to get 8.

$$-x=8$$

Multiply both sides by -1.

$$x=-8$$