Solve x+11/x+8+2x+15/x+10=3

$$\frac { x + 11 } { x + 8 } + \frac { 2 x + 15 } { x + 10 } = 3$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -10,-8 since division by zero is not defined. Multiply both sides of the equation by \left(x+8\right)\left(x+10\right), the least common multiple of x+8,x+10.

$$\left(x+10\right)\left(x+11\right)+\left(x+8\right)\left(2x+15\right)=3\left(x+8\right)\left(x+10\right)$$

Use the distributive property to multiply x+10 by x+11 and combine like terms.

$$x^{2}+21x+110+\left(x+8\right)\left(2x+15\right)=3\left(x+8\right)\left(x+10\right)$$

Use the distributive property to multiply x+8 by 2x+15 and combine like terms.

$$x^{2}+21x+110+2x^{2}+31x+120=3\left(x+8\right)\left(x+10\right)$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}+21x+110+31x+120=3\left(x+8\right)\left(x+10\right)$$

Combine 21x and 31x to get 52x.

$$3x^{2}+52x+110+120=3\left(x+8\right)\left(x+10\right)$$

Add 110 and 120 to get 230.

$$3x^{2}+52x+230=3\left(x+8\right)\left(x+10\right)$$

Use the distributive property to multiply 3 by x+8.

$$3x^{2}+52x+230=\left(3x+24\right)\left(x+10\right)$$

Use the distributive property to multiply 3x+24 by x+10 and combine like terms.

$$3x^{2}+52x+230=3x^{2}+54x+240$$

Subtract 3x^{2} from both sides.

$$3x^{2}+52x+230-3x^{2}=54x+240$$

Combine 3x^{2} and -3x^{2} to get 0.

$$52x+230=54x+240$$

Subtract 54x from both sides.

$$52x+230-54x=240$$

Combine 52x and -54x to get -2x.

$$-2x+230=240$$

Subtract 230 from both sides.

$$-2x=240-230$$

Subtract 230 from 240 to get 10.

$$-2x=10$$

Divide both sides by -2.

$$x=\frac{10}{-2}$$

Divide 10 by -2 to get -5.

$$x=-5$$