Solve for x (6x)/(x-3)=(4x+6)/(x-3)

$\frac{6 x}{x - 3} = \frac{4 x + 6}{x - 3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$6 x = 4 x + 6$

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$6 x - 4 x = 6$

Subtract $4 x$ from $6 x$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

Exclude the solutions that do not make $\frac{6 x}{x - 3} = \frac{4 x + 6}{x - 3}$ true.

$No solution$