Solve 55/x=15/x+20

$$5 \frac { 5 } { x } = \frac { 15 } { x + 20 }$$

Solve for x

$$x=-50$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -20,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+20\right), the least common multiple of x,x+20.

$$5\left(x+20\right)\times 5=x\times 15$$

Multiply 5 and 5 to get 25.

$$25\left(x+20\right)=x\times 15$$

Use the distributive property to multiply 25 by x+20.

$$25x+500=x\times 15$$

Subtract x\times 15 from both sides.

$$25x+500-x\times 15=0$$

Combine 25x and -x\times 15 to get 10x.

$$10x+500=0$$

Subtract 500 from both sides. Anything subtracted from zero gives its negation.

$$10x=-500$$

Divide both sides by 10.

$$x=\frac{-500}{10}$$

Divide -500 by 10 to get -50.

$$x=-50$$