Solve x-1/x+7+x+6/x+4=2

$$\frac { x - 1 } { x + 7 } + \frac { x + 6 } { x + 4 } = 2$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -7,-4 since division by zero is not defined. Multiply both sides of the equation by \left(x+4\right)\left(x+7\right), the least common multiple of x+7,x+4.

$$\left(x+4\right)\left(x-1\right)+\left(x+7\right)\left(x+6\right)=2\left(x+4\right)\left(x+7\right)$$

Use the distributive property to multiply x+4 by x-1 and combine like terms.

$$x^{2}+3x-4+\left(x+7\right)\left(x+6\right)=2\left(x+4\right)\left(x+7\right)$$

Use the distributive property to multiply x+7 by x+6 and combine like terms.

$$x^{2}+3x-4+x^{2}+13x+42=2\left(x+4\right)\left(x+7\right)$$

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

$$2x^{2}+3x-4+13x+42=2\left(x+4\right)\left(x+7\right)$$

Combine 3x and 13x to get 16x.

$$2x^{2}+16x-4+42=2\left(x+4\right)\left(x+7\right)$$

Add -4 and 42 to get 38.

$$2x^{2}+16x+38=2\left(x+4\right)\left(x+7\right)$$

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

$$2x^{2}+16x+38=\left(2x+8\right)\left(x+7\right)$$

Use the distributive property to multiply 2x+8 by x+7 and combine like terms.

$$2x^{2}+16x+38=2x^{2}+22x+56$$

Subtract 2x^{2} from both sides.

$$2x^{2}+16x+38-2x^{2}=22x+56$$

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

$$16x+38=22x+56$$

Subtract 22x from both sides.

$$16x+38-22x=56$$

Combine 16x and -22x to get -6x.

$$-6x+38=56$$

Subtract 38 from both sides.

$$-6x=56-38$$

Subtract 38 from 56 to get 18.

$$-6x=18$$

Divide both sides by -6.

$$x=\frac{18}{-6}$$

Divide 18 by -6 to get -3.

$$x=-3$$