Simplify the following fractions:
`(9g-6h)/(6g-4h)`

Answer

To simplify the fraction \((9g - 6h)/(6g - 4h)\), we will follow these steps:

### Step 1: Factor out the common terms from the numerator and the denominator.

**Numerator:**
- The expression is \(9g - 6h\).
- We can factor out \(3\) from both terms:
\[ 9g - 6h = 3(3g - 2h) \]

**Denominator:**
- The expression is \(6g - 4h\).
- We can factor out \(2\) from both terms:
\[ 6g - 4h = 2(3g - 2h) \]

### Step 2: Rewrite the fraction with the factored forms.

Now we can rewrite the original fraction:
\[ \frac{9g - 6h}{6g - 4h} = \frac{3(3g - 2h)}{2(3g - 2h)} \]

### Step 3: Cancel the common factors.

Since \(3g - 2h\) is present in both the numerator and the denominator, we can cancel it out:
\[ \frac{3(3g - 2h)}{2(3g - 2h)} = \frac{3}{2} \]

### Final Answer:
Thus, the simplified form of the fraction \((9g - 6h)/(6g - 4h)\) is:
\[ \frac{3}{2} \]

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