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

Question

$\frac{49m}{35n}:\frac{2n}{7m}-(\frac{2m^2}{n^2}-4)=\text{?}$

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:12 Negative times positive is always negative

00:17 Negative times negative is always positive

00:23 Let's factor 35 into 7 and 5

00:27 Let's reduce what we can

00:44 Divide 49 by 10

00:51 Let's use the commutative law and arrange the exercise

00:54 And this is the solution to the question

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 $2.9\frac{m^2}{n^2} + 4$ .

$2.9\frac{m^2}{n^2}+4$