Compute the difference indicated and simplify your answer. $$ \frac{5}{12}-\frac{3}{21} $$

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UpStudy AI · Accepted Answer

To compute the difference $$\frac{5}{12} - \frac{3}{21}$$ and simplify the result, follow these steps:

1. **Find a Common Denominator:**
   - The denominators are 12 and 21.
   - Factorize each:
     - $$12 = 2^2 \times 3$$
     - $$21 = 3 \times 7$$
   - The least common multiple (LCM) is $$2^2 \times 3 \times 7 = 84$$.

2. **Convert Each Fraction to the Common Denominator:**
   - $$\frac{5}{12} = \frac{5 \times 7}{12 \times 7} = \frac{35}{84}$$
   - $$\frac{3}{21} = \frac{3 \times 4}{21 \times 4} = \frac{12}{84}$$

3. **Subtract the Fractions:**
   $$
   \frac{35}{84} - \frac{12}{84} = \frac{35 - 12}{84} = \frac{23}{84}
   $$

4. **Simplify the Fraction:**
   - The numerator 23 is a prime number and does not divide evenly into 84.
   - Therefore, $$\frac{23}{84}$$ is already in its simplest form.

**Final Answer:**
$$
\frac{23}{84}
$$
$$ \frac{23}{84} $$

Compute the difference indicated and simplify your answer. \[ \frac{5}{12}-\frac{3}{21} \]

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