Question

divide and simplify.\\(\frac{14m^2n^2 + 35m^2n - 35mn^2}{14m^2n^2}\\)

Explanation:

Step1: Split the fraction

Split the numerator into three separate fractions over the same denominator:
$$\frac{14m^2n^2}{14m^2n^2} + \frac{35m^2n}{14m^2n^2} - \frac{35mn^2}{14m^2n^2}$$

Step2: Simplify each fraction

• For the first fraction: $\frac{14m^2n^2}{14m^2n^2} = 1$
• For the second fraction: Cancel common factors. The GCD of 35 and 14 is 7, and for variables, $m^2n / m^2n^2 = 1 / n$. So $\frac{35m^2n}{14m^2n^2} = \frac{5}{2n}$
• For the third fraction: Cancel common factors. The GCD of 35 and 14 is 7, and for variables, $mn^2 / m^2n^2 = 1 / m$. So $\frac{35mn^2}{14m^2n^2} = \frac{5}{2m}$ (note the subtraction sign, so it becomes $-\frac{5}{2m}$)

Step3: Combine the simplified fractions

Combine the results: $1 + \frac{5}{2n} - \frac{5}{2m}$

Answer:

$1 + \frac{5}{2n} - \frac{5}{2m}$ (or can be written as $1 + \frac{5m - 5n}{2mn}$ after getting a common denominator, but the first form is also simplified)