Algebra Examples

$\frac{40 m^{3} n^{4} - 24 m^{2} n^{7}}{8 m^{2} n^{5}}$

Step 1

Factor $8 m^{2} n^{4}$ out of $40 m^{3} n^{4} - 24 m^{2} n^{7}$ .

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Step 1.1

Factor $8 m^{2} n^{4}$ out of $40 m^{3} n^{4}$ .

$\frac{8 m^{2} n^{4} (5 m) - 24 m^{2} n^{7}}{8 m^{2} n^{5}}$

Step 1.2

Factor $8 m^{2} n^{4}$ out of $- 24 m^{2} n^{7}$ .

$\frac{8 m^{2} n^{4} (5 m) + 8 m^{2} n^{4} (- 3 n^{3})}{8 m^{2} n^{5}}$

Step 1.3

Factor $8 m^{2} n^{4}$ out of $8 m^{2} n^{4} (5 m) + 8 m^{2} n^{4} (- 3 n^{3})$ .

$\frac{8 m^{2} n^{4} (5 m - 3 n^{3})}{8 m^{2} n^{5}}$

Step 2

Cancel the common factor of $8$ .

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Step 2.1

Cancel the common factor.

$\frac{8 m^{2} n^{4} (5 m - 3 n^{3})}{8 m^{2} n^{5}}$

Step 2.2

Rewrite the expression.

$\frac{m^{2} n^{4} (5 m - 3 n^{3})}{m^{2} n^{5}}$

Step 3

Cancel the common factor of $m^{2}$ .

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Step 3.1

Cancel the common factor.

$\frac{m^{2} n^{4} (5 m - 3 n^{3})}{m^{2} n^{5}}$

Step 3.2

Rewrite the expression.

$\frac{n^{4} (5 m - 3 n^{3})}{n^{5}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $n^{4}$ out of $n^{5}$ .

$\frac{n^{4} (5 m - 3 n^{3})}{n^{4} n}$

Step 4.2

Cancel the common factor.

$\frac{n^{4} (5 m - 3 n^{3})}{n^{4} n}$

Step 4.3

Rewrite the expression.

$\frac{5 m - 3 n^{3}}{n}$

Step 5

Split the fraction $\frac{5 m - 3 n^{3}}{n}$ into two fractions.

$\frac{5 m}{n} + \frac{- 3 n^{3}}{n}$

Step 6

Cancel the common factor of $n^{3}$ and $n$ .

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Step 6.1

Factor $n$ out of $- 3 n^{3}$ .

$\frac{5 m}{n} + \frac{n (- 3 n^{2})}{n}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Raise $n$ to the power of $1$ .

$\frac{5 m}{n} + \frac{n (- 3 n^{2})}{n^{1}}$

Step 6.2.2

Factor $n$ out of $n^{1}$ .

$\frac{5 m}{n} + \frac{n (- 3 n^{2})}{n \cdot 1}$

Step 6.2.3

Cancel the common factor.

$\frac{5 m}{n} + \frac{n (- 3 n^{2})}{n \cdot 1}$

Step 6.2.4

Rewrite the expression.

$\frac{5 m}{n} + \frac{- 3 n^{2}}{1}$

Step 6.2.5

Divide $- 3 n^{2}$ by $1$ .

$\frac{5 m}{n} - 3 n^{2}$