Basic Math Examples

$\frac{a^{2} + 2 a - 15}{12 u} \cdot \frac{a u - 2 u}{a^{2} + 3 a - 10}$

Step 1

Factor $a^{2} + 2 a - 15$ using the AC method.

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Step 1.1

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 $- 15$ and whose sum is $2$ .

$- 3, 5$

Step 1.2

Write the factored form using these integers.

$\frac{(a - 3) (a + 5)}{12 u} \cdot \frac{a u - 2 u}{a^{2} + 3 a - 10}$

Step 2

Factor $u$ out of $a u - 2 u$ .

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Step 2.1

Factor $u$ out of $a u$ .

$\frac{(a - 3) (a + 5)}{12 u} \cdot \frac{u a - 2 u}{a^{2} + 3 a - 10}$

Step 2.2

Factor $u$ out of $- 2 u$ .

$\frac{(a - 3) (a + 5)}{12 u} \cdot \frac{u a + u \cdot - 2}{a^{2} + 3 a - 10}$

Step 2.3

Factor $u$ out of $u a + u \cdot - 2$ .

$\frac{(a - 3) (a + 5)}{12 u} \cdot \frac{u (a - 2)}{a^{2} + 3 a - 10}$

Step 3

Factor $a^{2} + 3 a - 10$ using the AC method.

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Step 3.1

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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Step 3.2

Write the factored form using these integers.

$\frac{(a - 3) (a + 5)}{12 u} \cdot \frac{u (a - 2)}{(a - 2) (a + 5)}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $a + 5$ .

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Step 4.1.1

Factor $a + 5$ out of $(a - 3) (a + 5)$ .

$\frac{(a + 5) (a - 3)}{12 u} \cdot \frac{u (a - 2)}{(a - 2) (a + 5)}$

Step 4.1.2

Factor $a + 5$ out of $(a - 2) (a + 5)$ .

$\frac{(a + 5) (a - 3)}{12 u} \cdot \frac{u (a - 2)}{(a + 5) (a - 2)}$

Step 4.1.3

Cancel the common factor.

$\frac{(a + 5) (a - 3)}{12 u} \cdot \frac{u (a - 2)}{(a + 5) (a - 2)}$

Step 4.1.4

Rewrite the expression.

$\frac{a - 3}{12 u} \cdot \frac{u (a - 2)}{a - 2}$

Step 4.2

Cancel the common factor of $u$ .

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Step 4.2.1

Factor $u$ out of $12 u$ .

$\frac{a - 3}{u \cdot 12} \cdot \frac{u (a - 2)}{a - 2}$

Step 4.2.2

Cancel the common factor.

$\frac{a - 3}{u \cdot 12} \cdot \frac{u (a - 2)}{a - 2}$

Step 4.2.3

Rewrite the expression.

$\frac{a - 3}{12} \cdot \frac{a - 2}{a - 2}$

Step 4.3

Multiply $\frac{a - 3}{12}$ by $\frac{a - 2}{a - 2}$ .

$\frac{(a - 3) (a - 2)}{12 (a - 2)}$

Step 4.4

Cancel the common factor of $a - 2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{(a - 3) (a - 2)}{12 (a - 2)}$

Step 4.4.2

Rewrite the expression.

$\frac{a - 3}{12}$