Solve x+3/x+7=x+6/x+4

$$\frac { x + 3 } { x + 7 } = \frac { x + 6 } { x + 4 }$$

Solve for x

$$x=-5$$

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.

$$\left(x+4\right)\left(x+3\right)=\left(x+7\right)\left(x+6\right)$$

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

$$x^{2}+7x+12=\left(x+7\right)\left(x+6\right)$$

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

$$x^{2}+7x+12=x^{2}+13x+42$$

Subtract x^{2} from both sides.

$$x^{2}+7x+12-x^{2}=13x+42$$

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

$$7x+12=13x+42$$

Subtract 13x from both sides.

$$7x+12-13x=42$$

Combine 7x and -13x to get -6x.

$$-6x+12=42$$

Subtract 12 from both sides.

$$-6x=42-12$$

Subtract 12 from 42 to get 30.

$$-6x=30$$

Divide both sides by -6.

$$x=\frac{30}{-6}$$

Divide 30 by -6 to get -5.

$$x=-5$$