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.