Solve 7/x-2/x-3=6/x

$$\frac { 7 } { x } - \frac { 2 } { x - 3 } = \frac { 6 } { x }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x,x-3.

$$\left(x-3\right)\times 7-x\times 2=\left(x-3\right)\times 6$$

Use the distributive property to multiply x-3 by 7.

$$7x-21-x\times 2=\left(x-3\right)\times 6$$

Use the distributive property to multiply x-3 by 6.

$$7x-21-x\times 2=6x-18$$

Subtract 6x from both sides.

$$7x-21-x\times 2-6x=-18$$

Combine 7x and -6x to get x.

$$x-21-x\times 2=-18$$

Add 21 to both sides.

$$x-x\times 2=-18+21$$

Add -18 and 21 to get 3.

$$x-x\times 2=3$$

Multiply -1 and 2 to get -2.

$$x-2x=3$$

Combine x and -2x to get -x.

$$-x=3$$

Multiply both sides by -1.

$$x=-3$$