Solve for X in (5+3x)/x = 3/4: Rational Equation Solution

Let's solve the equation $\frac{5+3x}{x} = \frac{3}{4}$.

• Step 1: Begin by applying cross-multiplication to eliminate the fractions. This gives us:

$(5 + 3x) \cdot 4 = 3 \cdot x$
Simplifying, we get:
$20 + 12x = 3x$

• Step 2: Rearrange the equation to bring all terms involving $x$ to one side:

$20 + 12x - 3x = 0$
Simplifying, we find:
$20 + 9x = 0$

• Step 3: Isolate $x$ by solving the equation:

$9x = -20$
Divide both sides by 9 to solve for $x$:
$x = -\frac{20}{9}$

Therefore, the solution to the equation $\frac{5+3x}{x} = \frac{3}{4}$ is $x = -\frac{20}{9}$.