Find if the given fractions are equivalent:
`42/(105), 36/(90)`

Answer

To determine if the fractions \( \frac{42}{105} \) and \( \frac{36}{90} \) are equivalent, we can simplify both fractions and see if they reduce to the same value.

### Step 1: Simplify \( \frac{42}{105} \)

1. **Find the GCD (Greatest Common Divisor)** of 42 and 105.
- The factors of 42 are: \( 1, 2, 3, 6, 7, 14, 21, 42 \)
- The factors of 105 are: \( 1, 3, 5, 7, 15, 21, 35, 105 \)
- The common factors are: \( 1, 3, 7, 21 \)
- The GCD is 21.

2. **Divide both the numerator and the denominator by the GCD**:
\[ \frac{42 \div 21}{105 \div 21} = \frac{2}{5} \]

### Step 2: Simplify \( \frac{36}{90} \)

1. **Find the GCD of 36 and 90**.
- The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The factors of 90 are: \( 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 \)
- The common factors are: \( 1, 2, 3, 6, 9, 18 \)
- The GCD is 18.

2. **Divide both the numerator and the denominator by the GCD**:
\[ \frac{36 \div 18}{90 \div 18} = \frac{2}{5} \]

### Conclusion:
Both fractions simplify to \( \frac{2}{5} \). Therefore, \( \frac{42}{105} \) and \( \frac{36}{90} \) are equivalent fractions.