Solve 4x/x^2+10x+24+x-3/x+4=x^2-8x+15/x^2+10x+24

$$\frac{ 4x }{ { x }^{ 2 } +10x+24 } + \frac{ x-3 }{ x+4 } = \frac{ { x }^{ 2 } -8x+15 }{ { x }^{ 2 } +10x+24 }$$

Solve for x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-4 since division by zero is not defined. Multiply both sides of the equation by \left(x+4\right)\left(x+6\right), the least common multiple of x^{2}+10x+24,x+4.

$$4x+\left(x+6\right)\left(x-3\right)=x^{2}-8x+15$$

Use the distributive property to multiply x+6 by x-3 and combine like terms.

$$4x+x^{2}+3x-18=x^{2}-8x+15$$

Combine 4x and 3x to get 7x.

$$7x+x^{2}-18=x^{2}-8x+15$$

Subtract x^{2} from both sides.

$$7x+x^{2}-18-x^{2}=-8x+15$$

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

$$7x-18=-8x+15$$

Add 8x to both sides.

$$7x-18+8x=15$$

Combine 7x and 8x to get 15x.

$$15x-18=15$$

Add 18 to both sides.

$$15x=15+18$$

Add 15 and 18 to get 33.

$$15x=33$$

Divide both sides by 15.

$$x=\frac{33}{15}$$

Reduce the fraction \frac{33}{15} to lowest terms by extracting and canceling out 3.

$$x=\frac{11}{5}$$