Basic Math Examples

$\frac{7 d^{2} - 14 d}{8 h^{5}} \cdot \frac{12 h^{3}}{21 d^{2} h - 28 d h^{2}}$

Step 1

Factor $7 d$ out of $7 d^{2} - 14 d$ .

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Step 1.1

Factor $7 d$ out of $7 d^{2}$ .

$\frac{7 d (d) - 14 d}{8 h^{5}} \cdot \frac{12 h^{3}}{21 d^{2} h - 28 d h^{2}}$

Step 1.2

Factor $7 d$ out of $- 14 d$ .

$\frac{7 d (d) + 7 d (- 2)}{8 h^{5}} \cdot \frac{12 h^{3}}{21 d^{2} h - 28 d h^{2}}$

Step 1.3

Factor $7 d$ out of $7 d (d) + 7 d (- 2)$ .

$\frac{7 d (d - 2)}{8 h^{5}} \cdot \frac{12 h^{3}}{21 d^{2} h - 28 d h^{2}}$

Step 2

Factor $7 d h$ out of $21 d^{2} h - 28 d h^{2}$ .

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Step 2.1

Factor $7 d h$ out of $21 d^{2} h$ .

$\frac{7 d (d - 2)}{8 h^{5}} \cdot \frac{12 h^{3}}{7 d h (3 d) - 28 d h^{2}}$

Step 2.2

Factor $7 d h$ out of $- 28 d h^{2}$ .

$\frac{7 d (d - 2)}{8 h^{5}} \cdot \frac{12 h^{3}}{7 d h (3 d) + 7 d h (- 4 h)}$

Step 2.3

Factor $7 d h$ out of $7 d h (3 d) + 7 d h (- 4 h)$ .

$\frac{7 d (d - 2)}{8 h^{5}} \cdot \frac{12 h^{3}}{7 d h (3 d - 4 h)}$

Step 3

Combine.

$\frac{7 d (d - 2) (12 h^{3})}{8 h^{5} (7 d h (3 d - 4 h))}$

Step 4

Multiply $h^{5}$ by $h$ by adding the exponents.

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Step 4.1

Move $h$ .

$\frac{7 d (d - 2) (12 h^{3})}{8 (h \cdot h^{5}) (7 d (3 d - 4 h))}$

Step 4.2

Multiply $h$ by $h^{5}$ .

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Step 4.2.1

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

$\frac{7 d (d - 2) (12 h^{3})}{8 (h^{1} h^{5}) (7 d (3 d - 4 h))}$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 d (d - 2) (12 h^{3})}{8 h^{1 + 5} (7 d (3 d - 4 h))}$

Step 4.3

Add $1$ and $5$ .

$\frac{7 d (d - 2) (12 h^{3})}{8 h^{6} (7 d (3 d - 4 h))}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$\frac{7 d (d - 2) (12 h^{3})}{8 h^{6} (7 d (3 d - 4 h))}$

Step 5.2

Rewrite the expression.

$\frac{(d (d - 2)) (12 h^{3})}{8 h^{6} (d (3 d - 4 h))}$

Step 6

Cancel the common factor of $d$ .

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Step 6.1

Cancel the common factor.

$\frac{d (d - 2) (12 h^{3})}{8 h^{6} (d (3 d - 4 h))}$

Step 6.2

Rewrite the expression.

$\frac{(d - 2) (12 h^{3})}{8 h^{6} (3 d - 4 h)}$

Step 7

Cancel the common factor of $12$ and $8$ .

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Step 7.1

Factor $4$ out of $(d - 2) (12 h^{3})$ .

$\frac{4 ((d - 2) (3 h^{3}))}{8 h^{6} (3 d - 4 h)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $8 h^{6} (3 d - 4 h)$ .

$\frac{4 ((d - 2) (3 h^{3}))}{4 (2 h^{6} (3 d - 4 h))}$

Step 7.2.2

Cancel the common factor.

$\frac{4 ((d - 2) (3 h^{3}))}{4 (2 h^{6} (3 d - 4 h))}$

Step 7.2.3

Rewrite the expression.

$\frac{(d - 2) (3 h^{3})}{2 h^{6} (3 d - 4 h)}$

Step 8

Cancel the common factor of $h^{3}$ and $h^{6}$ .

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Step 8.1

Factor $h^{3}$ out of $(d - 2) (3 h^{3})$ .

$\frac{h^{3} ((d - 2) \cdot (3))}{2 h^{6} (3 d - 4 h)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $h^{3}$ out of $2 h^{6} (3 d - 4 h)$ .

$\frac{h^{3} ((d - 2) \cdot (3))}{h^{3} (2 h^{3} (3 d - 4 h))}$

Step 8.2.2

Cancel the common factor.

$\frac{h^{3} ((d - 2) \cdot (3))}{h^{3} (2 h^{3} (3 d - 4 h))}$

Step 8.2.3

Rewrite the expression.

$\frac{(d - 2) \cdot (3)}{2 h^{3} (3 d - 4 h)}$

Step 9

Move $3$ to the left of $d - 2$ .

$\frac{3 (d - 2)}{2 h^{3} (3 d - 4 h)}$