Basic Math Examples

$\frac{\frac{4 h - 12}{4}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1

Cancel the common factor of $4 h - 12$ and $4$ .

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Step 1.1

Factor $4$ out of $4 h$ .

$\frac{\frac{4 (h) - 12}{4}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.2

Factor $4$ out of $- 12$ .

$\frac{\frac{4 (h) + 4 \cdot - 3}{4}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.3

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

$\frac{\frac{4 (h - 3)}{4}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $4$ out of $4$ .

$\frac{\frac{4 (h - 3)}{4 (1)}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.4.2

Cancel the common factor.

$\frac{\frac{4 (h - 3)}{4 \cdot 1}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.4.3

Rewrite the expression.

$\frac{\frac{h - 3}{1}}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 1.4.4

Divide $h - 3$ by $1$ .

$\frac{h - 3}{\frac{h^{2} - 7 h + 12}{9 h^{3} + 90 h^{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(h - 3) \frac{9 h^{3} + 90 h^{2}}{h^{2} - 7 h + 12}$

Step 3

Factor $9 h^{2}$ out of $9 h^{3} + 90 h^{2}$ .

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Step 3.1

Factor $9 h^{2}$ out of $9 h^{3}$ .

$(h - 3) \frac{9 h^{2} (h) + 90 h^{2}}{h^{2} - 7 h + 12}$

Step 3.2

Factor $9 h^{2}$ out of $90 h^{2}$ .

$(h - 3) \frac{9 h^{2} (h) + 9 h^{2} (10)}{h^{2} - 7 h + 12}$

Step 3.3

Factor $9 h^{2}$ out of $9 h^{2} (h) + 9 h^{2} (10)$ .

$(h - 3) \frac{9 h^{2} (h + 10)}{h^{2} - 7 h + 12}$

Step 4

Factor $h^{2} - 7 h + 12$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $12$ and whose sum is $- 7$ .

$- 4, - 3$

Step 4.2

Write the factored form using these integers.

$(h - 3) \frac{9 h^{2} (h + 10)}{(h - 4) (h - 3)}$

Step 5

Cancel the common factor of $h - 3$ .

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Step 5.1

Factor $h - 3$ out of $(h - 4) (h - 3)$ .

$(h - 3) \frac{9 h^{2} (h + 10)}{(h - 3) (h - 4)}$

Step 5.2

Cancel the common factor.

$(h - 3) \frac{9 h^{2} (h + 10)}{(h - 3) (h - 4)}$

Step 5.3

Rewrite the expression.

$\frac{9 h^{2} (h + 10)}{h - 4}$