Basic Math Examples

$\frac{\frac{\frac{a + 2}{a^{2} + 2 a - 3}}{a + 2}}{a^{2} - a}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{a + 2}{a^{2} + 2 a - 3}}{a + 2} \cdot \frac{1}{a^{2} - a}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{a + 2}{a^{2} + 2 a - 3} \cdot \frac{1}{a + 2} \frac{1}{a^{2} - a}$

Step 3

Cancel the common factor of $a + 2$ .

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Step 3.1

Cancel the common factor.

$\frac{a + 2}{a^{2} + 2 a - 3} \cdot \frac{1}{a + 2} \frac{1}{a^{2} - a}$

Step 3.2

Rewrite the expression.

$\frac{1}{a^{2} + 2 a - 3} \cdot \frac{1}{a^{2} - a}$

Step 4

Factor $a^{2} + 2 a - 3$ 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 $- 3$ and whose sum is $2$ .

$- 1, 3$

Step 4.2

Write the factored form using these integers.

$\frac{1}{(a - 1) (a + 3)} \cdot \frac{1}{a^{2} - a}$

Step 5

Factor $a$ out of $a^{2} - a$ .

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Step 5.1

Factor $a$ out of $a^{2}$ .

$\frac{1}{(a - 1) (a + 3)} \cdot \frac{1}{a \cdot a - a}$

Step 5.2

Factor $a$ out of $- a$ .

$\frac{1}{(a - 1) (a + 3)} \cdot \frac{1}{a \cdot a + a \cdot - 1}$

Step 5.3

Factor $a$ out of $a \cdot a + a \cdot - 1$ .

$\frac{1}{(a - 1) (a + 3)} \cdot \frac{1}{a (a - 1)}$

Step 6

Multiply $\frac{1}{(a - 1) (a + 3)} \cdot \frac{1}{a (a - 1)}$ .

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Step 6.1

Multiply $\frac{1}{(a - 1) (a + 3)}$ by $\frac{1}{a (a - 1)}$ .

$\frac{1}{(a - 1) (a + 3) (a (a - 1))}$

Step 6.2

Raise $a - 1$ to the power of $1$ .

$\frac{1}{(a + 3) (a ({(a - 1)}^{1} (a - 1)))}$

Step 6.3

Raise $a - 1$ to the power of $1$ .

$\frac{1}{(a + 3) (a ({(a - 1)}^{1} {(a - 1)}^{1}))}$

Step 6.4

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

$\frac{1}{(a + 3) (a {(a - 1)}^{1 + 1})}$

Step 6.5

Add $1$ and $1$ .

$\frac{1}{(a + 3) (a {(a - 1)}^{2})}$

Step 7

Reorder factors in $\frac{1}{(a + 3) a {(a - 1)}^{2}}$ .

$\frac{1}{a (a + 3) {(a - 1)}^{2}}$