Solve the Fraction Equation: 7/5 - 7/15 - 1/3

To solve this problem, we'll follow these steps:

• Step 1: Identify the least common multiple (LCM) for the denominators 5, 15, and 3.
• Step 2: Convert each fraction to equivalent fractions with the common denominator.
• Step 3: Perform subtraction on these equivalent fractions.

Let's work through each step:

Step 1: The denominators are 5, 15, and 3. The LCM of these numbers is 15, as it is the smallest number that all denominators divide evenly.

Step 2:

• Convert $\frac{7}{5}$ to an equivalent fraction with a denominator of 15: $\frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15}$.
• $\frac{7}{15}$ already has the denominator 15.
• Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 15: $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$.

Step 3: Subtract the fractions:

$\frac{21}{15} - \frac{7}{15} - \frac{5}{15} = \frac{21 - 7 - 5}{15} = \frac{9}{15}.$

Simplify $\frac{9}{15}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:

$\frac{9 \div 3}{15 \div 3} = \frac{3}{5}.$

Therefore, the solution to the problem is $\frac{3}{5}$.