Solve x/x+2+4/x+6=1

$$\frac { x } { x + 2 } + \frac { 4 } { x + 6 } = 1$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

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

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

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

$$x^{2}+6x+4x+8=\left(x+2\right)\left(x+6\right)$$

Combine 6x and 4x to get 10x.

$$x^{2}+10x+8=\left(x+2\right)\left(x+6\right)$$

Use the distributive property to multiply x+2 by x+6 and combine like terms.

$$x^{2}+10x+8=x^{2}+8x+12$$

Subtract x^{2} from both sides.

$$x^{2}+10x+8-x^{2}=8x+12$$

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

$$10x+8=8x+12$$

Subtract 8x from both sides.

$$10x+8-8x=12$$

Combine 10x and -8x to get 2x.

$$2x+8=12$$

Subtract 8 from both sides.

$$2x=12-8$$

Subtract 8 from 12 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$