Solve for x (5x)/(x-2)=(3x+4)/(x-2)

$\frac{5 x}{x - 2} = \frac{3 x + 4}{x - 2}$

Step 1

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

$5 x = 3 x + 4$

Step 2

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

Subtract $3 x$ from both sides of the equation.

$5 x - 3 x = 4$

Subtract $3 x$ from $5 x$ .

$2 x = 4$

Step 3

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

Step 4

Exclude the solutions that do not make $\frac{5 x}{x - 2} = \frac{3 x + 4}{x - 2}$ true.

$No solution$