Solve x+3/x+4=x+3/x+2

$$\frac { x + 3 } { x + 4 } = \frac { x + 3 } { x + 2 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,-2 since division by zero is not defined. Multiply both sides of the equation by \left(x+2\right)\left(x+4\right), the least common multiple of x+4,x+2.

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

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$x^{2}+5x+6=\left(x+4\right)\left(x+3\right)$$

Use the distributive property to multiply x+4 by x+3 and combine like terms.

$$x^{2}+5x+6=x^{2}+7x+12$$

Subtract x^{2} from both sides.

$$x^{2}+5x+6-x^{2}=7x+12$$

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

$$5x+6=7x+12$$

Subtract 7x from both sides.

$$5x+6-7x=12$$

Combine 5x and -7x to get -2x.

$$-2x+6=12$$

Subtract 6 from both sides.

$$-2x=12-6$$

Subtract 6 from 12 to get 6.

$$-2x=6$$

Divide both sides by -2.

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

Divide 6 by -2 to get -3.

$$x=-3$$