`(6)/(x)=(4)/(x-9)`, what is the value of `(x)/(18)`?

Options

A. `3`
B. `2`
C. `(1)/(2)`
D. `(3)/(2)`

Answer

To solve the equation \(\frac{6}{x} = \frac{4}{x - 9}\) and find the value of \(\frac{x}{18}\), we can follow these steps:

### Step 1: Cross Multiply
We start by cross multiplying the fractions to eliminate the denominators:
\[ 6(x - 9) = 4x \]

### Step 2: Distribute
Next, we distribute \(6\) on the left side:
\[ 6x - 54 = 4x \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\). We move \(4x\) to the left side:
\[ 6x - 4x = 54 \]
This simplifies to:
\[ 2x = 54 \]

### Step 4: Solve for \(x\)
Now, we divide both sides by \(2\) to solve for \(x\):
\[ x = \frac{54}{2} = 27 \]

### Step 5: Find \(\frac{x}{18}\)
Now that we have \(x\), we can find \(\frac{x}{18}\):
\[ \frac{x}{18} = \frac{27}{18} \]

### Step 6: Simplify
We simplify \(\frac{27}{18}\):
\[ \frac{27}{18} = \frac{3}{2} \]

Thus, the final answer is:
\[ \frac{x}{18} = \frac{3}{2} \]