Solve 10/x-3-3=12/3x-9

$$\frac{ 10 }{ x-3 } -3= \frac{ 12 }{ 3x-9 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-3\right), the least common multiple of x-3,3x-9.

$$3\times 10+3\left(x-3\right)\left(-3\right)=12$$

Multiply 3 and 10 to get 30.

$$30+3\left(x-3\right)\left(-3\right)=12$$

Multiply 3 and -3 to get -9.

$$30-9\left(x-3\right)=12$$

Use the distributive property to multiply -9 by x-3.

$$30-9x+27=12$$

Add 30 and 27 to get 57.

$$57-9x=12$$

Subtract 57 from both sides.

$$-9x=12-57$$

Subtract 57 from 12 to get -45.

$$-9x=-45$$

Divide both sides by -9.

$$x=\frac{-45}{-9}$$

Divide -45 by -9 to get 5.

$$x=5$$