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

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

Solve for x

$$x = -\frac{27}{7} = -3\frac{6}{7} \approx -3.857142857$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-4 since division by zero is not defined. Multiply both sides of the equation by \left(x+4\right)\left(x+5\right), the least common multiple of x+4,x+5.

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

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15=\left(x+4\right)\left(x-3\right)$$

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

$$x^{2}+8x+15=x^{2}+x-12$$

Subtract x^{2} from both sides.

$$x^{2}+8x+15-x^{2}=x-12$$

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

$$8x+15=x-12$$

Subtract x from both sides.

$$8x+15-x=-12$$

Combine 8x and -x to get 7x.

$$7x+15=-12$$

Subtract 15 from both sides.

$$7x=-12-15$$

Subtract 15 from -12 to get -27.

$$7x=-27$$

Divide both sides by 7.

$$x=\frac{-27}{7}$$

Fraction \frac{-27}{7} can be rewritten as -\frac{27}{7} by extracting the negative sign.

$$x=-\frac{27}{7}$$