Solve 2/x-9=9/x+12

$$\frac { 2 } { x - 9 } = \frac { 9 } { x + 12 }$$

Solve for x

$$x=15$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -12,9 since division by zero is not defined. Multiply both sides of the equation by \left(x-9\right)\left(x+12\right), the least common multiple of x-9,x+12.

$$\left(x+12\right)\times 2=\left(x-9\right)\times 9$$

Use the distributive property to multiply x+12 by 2.

$$2x+24=\left(x-9\right)\times 9$$

Use the distributive property to multiply x-9 by 9.

$$2x+24=9x-81$$

Subtract 9x from both sides.

$$2x+24-9x=-81$$

Combine 2x and -9x to get -7x.

$$-7x+24=-81$$

Subtract 24 from both sides.

$$-7x=-81-24$$

Subtract 24 from -81 to get -105.

$$-7x=-105$$

Divide both sides by -7.

$$x=\frac{-105}{-7}$$

Divide -105 by -7 to get 15.

$$x=15$$