If `(5)/(x)=(9)/(x+2)`, what is the value of `(x)/(3)`?

Answer

To solve the equation \(\frac{5}{x} = \frac{9}{x+2}\) and find the value of \(\frac{x}{3}\), we can follow these steps:

### Step 1: Cross Multiply
We start by cross multiplying to eliminate the fractions:
\[ 5(x + 2) = 9x \]

### Step 2: Distribute
Next, we distribute \(5\) on the left side:
\[ 5x + 10 = 9x \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\). We can do this by subtracting \(5x\) from both sides:
\[ 10 = 9x - 5x \]
This simplifies to:
\[ 10 = 4x \]

### Step 4: Solve for \(x\)
Now, divide both sides by \(4\) to solve for \(x\):
\[ x = \frac{10}{4} = \frac{5}{2} \]

### Step 5: Find \(\frac{x}{3}\)
Now that we have \(x\), we can find \(\frac{x}{3}\):
\[ \frac{x}{3} = \frac{\frac{5}{2}}{3} \]
This can be rewritten as:
\[ \frac{5}{2} \cdot \frac{1}{3} = \frac{5}{6} \]

### Final Answer
Thus, the value of \(\frac{x}{3}\) is:
\[ \frac{5}{6} \]

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