Solve 6+x/15+x=20+x/43+x

$$\frac{ 6+x }{ 15+x } = \frac{ 20+x }{ 43+x }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -43,-15 since division by zero is not defined. Multiply both sides of the equation by \left(x+15\right)\left(x+43\right), the least common multiple of 15+x,43+x.

$$\left(x+43\right)\left(6+x\right)=\left(x+15\right)\left(20+x\right)$$

Use the distributive property to multiply x+43 by 6+x and combine like terms.

$$49x+x^{2}+258=\left(x+15\right)\left(20+x\right)$$

Use the distributive property to multiply x+15 by 20+x and combine like terms.

$$49x+x^{2}+258=35x+x^{2}+300$$

Subtract 35x from both sides.

$$49x+x^{2}+258-35x=x^{2}+300$$

Combine 49x and -35x to get 14x.

$$14x+x^{2}+258=x^{2}+300$$

Subtract x^{2} from both sides.

$$14x+x^{2}+258-x^{2}=300$$

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

$$14x+258=300$$

Subtract 258 from both sides.

$$14x=300-258$$

Subtract 258 from 300 to get 42.

$$14x=42$$

Divide both sides by 14.

$$x=\frac{42}{14}$$

Divide 42 by 14 to get 3.

$$x=3$$