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

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

Solve for x

$$x = -\frac{105}{4} = -26\frac{1}{4} = -26.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -20,-15 since division by zero is not defined. Multiply both sides of the equation by \left(x+15\right)\left(x+20\right), the least common multiple of 15+x,20+x.

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

Multiply x+15 and 15+x to get \left(x+15\right)^{2}.

$$\left(x+20\right)\left(6+x\right)=\left(x+15\right)^{2}$$

Use the distributive property to multiply x+20 by 6+x and combine like terms.

$$26x+x^{2}+120=\left(x+15\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+15\right)^{2}.

$$26x+x^{2}+120=x^{2}+30x+225$$

Subtract x^{2} from both sides.

$$26x+x^{2}+120-x^{2}=30x+225$$

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

$$26x+120=30x+225$$

Subtract 30x from both sides.

$$26x+120-30x=225$$

Combine 26x and -30x to get -4x.

$$-4x+120=225$$

Subtract 120 from both sides.

$$-4x=225-120$$

Subtract 120 from 225 to get 105.

$$-4x=105$$

Divide both sides by -4.

$$x=\frac{105}{-4}$$

Fraction \frac{105}{-4} can be rewritten as -\frac{105}{4} by extracting the negative sign.

$$x=-\frac{105}{4}$$