Solve 1/x-4=1/y-9

$$\frac { 1 } { x - 4 } = \frac { 1 } { y - 9 }$$

Solve for x

$$x=y-5$$

$$y\neq 9$$

Solution Steps

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(y-9\right), the least common multiple of x-4,y-9.

$$y-9=x-4$$

Swap sides so that all variable terms are on the left hand side.

$$x-4=y-9$$

Add 4 to both sides.

$$x=y-9+4$$

Add -9 and 4 to get -5.

$$x=y-5$$

Variable x cannot be equal to 4.

$$x=y-5\text{, }x\neq 4$$

Solve for y

$$y=x+5$$

$$x\neq 4$$

Solution Steps

Variable y cannot be equal to 9 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(y-9\right), the least common multiple of x-4,y-9.

$$y-9=x-4$$

Add 9 to both sides.

$$y=x-4+9$$

Add -4 and 9 to get 5.

$$y=x+5$$

Variable y cannot be equal to 9.

$$y=x+5\text{, }y\neq 9$$