Question

solve the equation. $\frac{3}{x}+\frac{1}{3x}=\frac{5}{9}$

Explanation:

Step1: Find common denominator

The common denominator of $x$ and $3x$ is $3x$. Rewrite the left side:
$\frac{3 \times 3}{3x} + \frac{1}{3x} = \frac{5}{9}$
$\frac{9}{3x} + \frac{1}{3x} = \frac{5}{9}$

Step2: Combine left side terms

Add the numerators over the common denominator:
$\frac{9 + 1}{3x} = \frac{5}{9}$
$\frac{10}{3x} = \frac{5}{9}$

Step3: Cross-multiply to eliminate fractions

Set product of extremes equal to means:
$10 \times 9 = 5 \times 3x$
$90 = 15x$

Step4: Solve for $x$

Divide both sides by 15:
$x = \frac{90}{15}$

Answer:

$x = 6$