Solve the Expression: 39÷(3x)+y/x÷y/4 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Simplify each division separately.
• Step 2: Combine the results.

Now, let's work through each step:

Step 1: Simplify $39 : (x \cdot 3)$.

This is equivalent to $\frac{39}{x \cdot 3} = \frac{39}{3x}$.

Step 2: Simplify $\frac{y}{x} : \frac{y}{4}$.

This is equivalent to $\frac{y}{x} \times \frac{4}{y} = \frac{4y}{xy} = \frac{4}{x}$.

Step 3: Add the results from Steps 1 and 2.

We have:

$\frac{39}{3x} + \frac{4}{x}$

Simplifying further, find a common denominator for the fractions, which is $3x$:

$\frac{39}{3x} + \frac{4 \cdot 3}{3x} = \frac{39 + 12}{3x} = \frac{51}{3x} = \frac{17}{x}$.

Therefore, the solution to the problem is $\frac{17}{x}$.