Algebra Examples

$\frac{5 c^{2} - 15 c^{3}}{20 c^{2} d + 25 c^{2}}$

Step 1

Factor $5 c^{2}$ out of $5 c^{2} - 15 c^{3}$ .

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Step 1.1

Factor $5 c^{2}$ out of $5 c^{2}$ .

$\frac{5 c^{2} (1) - 15 c^{3}}{20 c^{2} d + 25 c^{2}}$

Step 1.2

Factor $5 c^{2}$ out of $- 15 c^{3}$ .

$\frac{5 c^{2} (1) + 5 c^{2} (- 3 c)}{20 c^{2} d + 25 c^{2}}$

Step 1.3

Factor $5 c^{2}$ out of $5 c^{2} (1) + 5 c^{2} (- 3 c)$ .

$\frac{5 c^{2} (1 - 3 c)}{20 c^{2} d + 25 c^{2}}$

Step 2

Factor $5 c^{2}$ out of $20 c^{2} d + 25 c^{2}$ .

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Step 2.1

Factor $5 c^{2}$ out of $20 c^{2} d$ .

$\frac{5 c^{2} (1 - 3 c)}{5 c^{2} (4 d) + 25 c^{2}}$

Step 2.2

Factor $5 c^{2}$ out of $25 c^{2}$ .

$\frac{5 c^{2} (1 - 3 c)}{5 c^{2} (4 d) + 5 c^{2} (5)}$

Step 2.3

Factor $5 c^{2}$ out of $5 c^{2} (4 d) + 5 c^{2} (5)$ .

$\frac{5 c^{2} (1 - 3 c)}{5 c^{2} (4 d + 5)}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 c^{2} (1 - 3 c)}{5 c^{2} (4 d + 5)}$

Step 3.2

Rewrite the expression.

$\frac{c^{2} (1 - 3 c)}{c^{2} (4 d + 5)}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{c^{2} (1 - 3 c)}{c^{2} (4 d + 5)}$

Step 4.2

Rewrite the expression.

$\frac{1 - 3 c}{4 d + 5}$