Solve x+4/x+3=x-2/x-5

$$\frac{ x+4 }{ x+3 } = \frac{ x-2 }{ x-5 }$$

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+3\right), the least common multiple of x+3,x-5.

$$\left(x-5\right)\left(x+4\right)=\left(x+3\right)\left(x-2\right)$$

Use the distributive property to multiply x-5 by x+4 and combine like terms.

$$x^{2}-x-20=\left(x+3\right)\left(x-2\right)$$

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

$$x^{2}-x-20=x^{2}+x-6$$

Subtract x^{2} from both sides.

$$x^{2}-x-20-x^{2}=x-6$$

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

$$-x-20=x-6$$

Subtract x from both sides.

$$-x-20-x=-6$$

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

$$-2x-20=-6$$

Add 20 to both sides.

$$-2x=-6+20$$

Add -6 and 20 to get 14.

$$-2x=14$$

Divide both sides by -2.

$$x=\frac{14}{-2}$$

Divide 14 by -2 to get -7.

$$x=-7$$