Solve 1/x+10+18/x+8=-8/x+10

$$\frac { 1 } { x + 10 } + \frac { 18 } { x + 8 } = - \frac { 8 } { x + 10 }$$

Solve for x

$$x = -\frac{28}{3} = -9\frac{1}{3} \approx -9.333333333$$

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+10,x+8.

$$x+8+\left(x+10\right)\times 18=-\left(x+8\right)\times 8$$

Use the distributive property to multiply x+10 by 18.

$$x+8+18x+180=-\left(x+8\right)\times 8$$

Combine x and 18x to get 19x.

$$19x+8+180=-\left(x+8\right)\times 8$$

Add 8 and 180 to get 188.

$$19x+188=-\left(x+8\right)\times 8$$

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

$$19x+188=-\left(8x+64\right)$$

To find the opposite of 8x+64, find the opposite of each term.

$$19x+188=-8x-64$$

Add 8x to both sides.

$$19x+188+8x=-64$$

Combine 19x and 8x to get 27x.

$$27x+188=-64$$

Subtract 188 from both sides.

$$27x=-64-188$$

Subtract 188 from -64 to get -252.

$$27x=-252$$

Divide both sides by 27.

$$x=\frac{-252}{27}$$

Reduce the fraction \frac{-252}{27} to lowest terms by extracting and canceling out 9.

$$x=-\frac{28}{3}$$