Let's solve the equation \( a + \frac{4}{3} - \frac{9}{7} = a + \frac{7}{5} \).

### Step 1: Simplify both sides
First, subtract \( a \) from both sides of the equation:

\[
\frac{4}{3} - \frac{9}{7} = \frac{7}{5}
\]

### Step 2: Find a common denominator on the left side
To subtract the fractions \( \frac{4}{3} \) and \( \frac{9}{7} \), we need to find a common denominator:

- The common denominator between 3 and 7 is 21.

Convert each fraction:

\[
\frac{4}{3} = \frac{4 \times 7}{3 \times 7} = \frac{28}{21}
\]
\[
\frac{9}{7} = \frac{9 \times 3}{7 \times 3} = \frac{27}{21}
\]

So the left side becomes:

\[
\frac{28}{21} - \frac{27}{21} = \frac{1}{21}
\]

### Step 3: Equate both sides
Now we have:

\[
\frac{1}{21} = \frac{7}{5}
\]

### Step 4: Check for equality
These fractions are clearly not equal since their cross products are different:

\[
1 \times 5 = 5 \quad \text{and} \quad 21 \times 7 = 147
\]

Since \( \frac{1}{21} \neq \frac{7}{5} \), there is no value of \( a \) that satisfies this equation. Thus, the equation has no solution.

Would you like more details or have any other questions?

Here are five related questions you might consider:
1. How do you solve equations with variables on both sides?
2. What are the steps to find a common denominator?
3. How do you verify if two fractions are equivalent?
4. What are the rules for subtracting fractions?
5. How can you solve inequalities involving fractions?

**Tip:** Always double-check your arithmetic when dealing with fractions, especially when subtracting or finding common denominators.

Explore how to solve equations involving fractions step-by-step. This example covers common denominators, equality of fractions, and arithmetic with fractions. Suitable for high school students.

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