To simplify \(-\frac{30x^2}{105y^2}\), follow these steps:

### Step 1: Simplify the numerical part
First, simplify the fraction \(\frac{30}{105}\).

The greatest common divisor (GCD) of 30 and 105 is 15, so divide both the numerator and the denominator by 15:

\[
\frac{30}{105} = \frac{30 \div 15}{105 \div 15} = \frac{2}{7}
\]

### Step 2: Combine the variables
The variables \(x^2\) and \(y^2\) do not have any common factors, so they remain in the fraction.

### Step 3: Reapply the negative sign
So, after simplifying, we get:

\[
-\frac{30x^2}{105y^2} = -\frac{2x^2}{7y^2}
\]

Thus, the simplified expression is:

\[
-\frac{2x^2}{7y^2}
\]

Would you like any further details or clarification?

### Related questions:
1. How do you find the GCD of two numbers?
2. Can the variables in this fraction be simplified further in any case?
3. How do negative signs affect the simplification of fractions?
4. What happens if there are higher exponents in the terms?
5. How do you simplify fractions involving more complex expressions?

**Tip**: Always start by simplifying the numerical coefficients before dealing with the variables.

This step-by-step solution explains how to simplify the algebraic fraction -30x²/105y². Learn how to apply the greatest common divisor (GCD) to simplify fractions and handle algebraic variables. Perfect for students in Grades 7-9.

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