Solve : `(5)/(x)=(7)/(x-4)`

Answer

To solve the equation \(\frac{5}{x} = \frac{7}{x-4}\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying the fractions to eliminate the denominators:

\[ 5(x - 4) = 7x \]

### Step 2: Distribute
Next, we distribute \(5\) on the left side:

\[ 5x - 20 = 7x \]

### Step 3: Rearrange the Equation
Now, we will move all terms involving \(x\) to one side and constant terms to the other side. We can subtract \(5x\) from both sides:

\[ -20 = 7x - 5x \]

This simplifies to:

\[ -20 = 2x \]

### Step 4: Solve for \(x\)
Now, we divide both sides by \(2\) to isolate \(x\):

\[ x = \frac{-20}{2} \]

This gives us:

\[ x = -10 \]

### Final Solution
The solution to the equation \(\frac{5}{x} = \frac{7}{x-4}\) is:

\[ \boxed{-10} \]

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