Solve the Fraction Division and Polynomial Subtraction: 49m/35n : 2n/7m - (2m²/n² - 4)

To solve this problem, let's go through it step-by-step:

• Step 1: Simplify the division of fractions: $\frac{49m}{35n}:\frac{2n}{7m}$
• Step 2: This is equivalent to multiplying: $\frac{49m}{35n} \times \frac{7m}{2n}$
• Step 3: Simplify: Multiply numerators and denominators: $\frac{49 \cdot 7 \cdot m^2}{35 \cdot 2 \cdot n^2}$
• Step 4: Compute simplification: $\frac{343m^2}{70n^2} \rightarrow \frac{49m^2}{10n^2}$
• Step 5: Substitute back to expression: $\frac{49m^2}{10n^2} - (\frac{2m^2}{n^2} - 4)$
• Step 6: Express $\frac{2m^2}{n^2}$ in terms of 10 denominator: $\frac{20m^2}{10n^2}$
• Step 7: Calculate complete subtraction: $\frac{49m^2}{10n^2} - \frac{20m^2}{10n^2} + 4$
• Step 8: Simplify result: $\frac{29m^2}{10n^2} + 4$

Therefore, the solution to the problem is $2.9\frac{m^2}{n^2} + 4$.