Solve 28+x/x=28+y/y

$$\frac{ 28+x }{ x } = \frac{ 28+y }{ y }$$

Solve for x

$$x=y$$

$$y\neq 0$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.

$$y\left(28+x\right)=x\left(28+y\right)$$

Use the distributive property to multiply y by 28+x.

$$28y+yx=x\left(28+y\right)$$

Use the distributive property to multiply x by 28+y.

$$28y+yx=28x+xy$$

Subtract 28x from both sides.

$$28y+yx-28x=xy$$

Subtract xy from both sides.

$$28y+yx-28x-xy=0$$

Combine yx and -xy to get 0.

$$28y-28x=0$$

Subtract 28y from both sides. Anything subtracted from zero gives its negation.

$$-28x=-28y$$

Cancel out -28 on both sides.

$$x=y$$

Variable x cannot be equal to 0.

$$x=y\text{, }x\neq 0$$

Solve for y

$$y=x$$

$$x\neq 0$$

Solution Steps

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.

$$y\left(28+x\right)=x\left(28+y\right)$$

Use the distributive property to multiply y by 28+x.

$$28y+yx=x\left(28+y\right)$$

Use the distributive property to multiply x by 28+y.

$$28y+yx=28x+xy$$

Subtract xy from both sides.

$$28y+yx-xy=28x$$

Combine yx and -xy to get 0.

$$28y=28x$$

Cancel out 28 on both sides.

$$y=x$$

Variable y cannot be equal to 0.

$$y=x\text{, }y\neq 0$$