Algebra Examples

$\frac{20 n^{3} + 15 n^{2}}{20 n^{2} + 10 n}$

Step 1

Factor $5 n^{2}$ out of $20 n^{3} + 15 n^{2}$ .

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Step 1.1

Factor $5 n^{2}$ out of $20 n^{3}$ .

$\frac{5 n^{2} (4 n) + 15 n^{2}}{20 n^{2} + 10 n}$

Step 1.2

Factor $5 n^{2}$ out of $15 n^{2}$ .

$\frac{5 n^{2} (4 n) + 5 n^{2} (3)}{20 n^{2} + 10 n}$

Step 1.3

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

$\frac{5 n^{2} (4 n + 3)}{20 n^{2} + 10 n}$

Step 2

Factor $10 n$ out of $20 n^{2} + 10 n$ .

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Step 2.1

Factor $10 n$ out of $20 n^{2}$ .

$\frac{5 n^{2} (4 n + 3)}{10 n (2 n) + 10 n}$

Step 2.2

Factor $10 n$ out of $10 n$ .

$\frac{5 n^{2} (4 n + 3)}{10 n (2 n) + 10 n (1)}$

Step 2.3

Factor $10 n$ out of $10 n (2 n) + 10 n (1)$ .

$\frac{5 n^{2} (4 n + 3)}{10 n (2 n + 1)}$

Step 3

Cancel the common factor of $5$ and $10$ .

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Step 3.1

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

$\frac{5 (n^{2} (4 n + 3))}{10 n (2 n + 1)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $10 n (2 n + 1)$ .

$\frac{5 (n^{2} (4 n + 3))}{5 (2 n (2 n + 1))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (n^{2} (4 n + 3))}{5 (2 n (2 n + 1))}$

Step 3.2.3

Rewrite the expression.

$\frac{n^{2} (4 n + 3)}{2 n (2 n + 1)}$

Step 4

Cancel the common factor of $n^{2}$ and $n$ .

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Step 4.1

Factor $n$ out of $n^{2} (4 n + 3)$ .

$\frac{n (n (4 n + 3))}{2 n (2 n + 1)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $n$ out of $2 n (2 n + 1)$ .

$\frac{n (n (4 n + 3))}{n (2 (2 n + 1))}$

Step 4.2.2

Cancel the common factor.

$\frac{n (n (4 n + 3))}{n (2 (2 n + 1))}$

Step 4.2.3

Rewrite the expression.

$\frac{n (4 n + 3)}{2 (2 n + 1)}$