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

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

Solve for x

$$x=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

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

$$\left(x+2\right)x+\left(x-1\right)\times 6=\left(x-1\right)\left(x+2\right)$$

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

$$x^{2}+2x+\left(x-1\right)\times 6=\left(x-1\right)\left(x+2\right)$$

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

$$x^{2}+2x+6x-6=\left(x-1\right)\left(x+2\right)$$

Combine 2x and 6x to get 8x.

$$x^{2}+8x-6=\left(x-1\right)\left(x+2\right)$$

Use the distributive property to multiply x-1 by x+2 and combine like terms.

$$x^{2}+8x-6=x^{2}+x-2$$

Subtract x^{2} from both sides.

$$x^{2}+8x-6-x^{2}=x-2$$

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

$$8x-6=x-2$$

Subtract x from both sides.

$$8x-6-x=-2$$

Combine 8x and -x to get 7x.

$$7x-6=-2$$

Add 6 to both sides.

$$7x=-2+6$$

Add -2 and 6 to get 4.

$$7x=4$$

Divide both sides by 7.

$$x=\frac{4}{7}$$