Basic Math Examples

$\frac{6}{a} - 4 + \frac{a}{2}$

Step 1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{6}{a} - 4 \cdot \frac{a}{a} + \frac{a}{2}$

Step 2

Combine $- 4$ and $\frac{a}{a}$ .

$\frac{6}{a} + \frac{- 4 a}{a} + \frac{a}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 - 4 a}{a} + \frac{a}{2}$

Step 4

Factor $2$ out of $6 - 4 a$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{2 (3) - 4 a}{a} + \frac{a}{2}$

Step 4.2

Factor $2$ out of $- 4 a$ .

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

Step 4.3

Factor $2$ out of $2 (3) + 2 (- 2 a)$ .

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

Step 5

To write $\frac{2 (3 - 2 a)}{a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 6

To write $\frac{a}{2}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

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

Step 7

Write each expression with a common denominator of $a \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

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

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

Step 7.2

Multiply $\frac{a}{2}$ by $\frac{a}{a}$ .

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

Step 7.3

Reorder the factors of $a \cdot 2$ .

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

Step 8

Combine the numerators over the common denominator.

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

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

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

Step 9.2

Multiply $2$ by $3$ .

$\frac{(6 + 2 (- 2 a)) \cdot 2 + a \cdot a}{2 a}$

Step 9.3

Multiply $- 2$ by $2$ .

$\frac{(6 - 4 a) \cdot 2 + a \cdot a}{2 a}$

Step 9.4

Apply the distributive property.

$\frac{6 \cdot 2 - 4 a \cdot 2 + a \cdot a}{2 a}$

Step 9.5

Multiply $6$ by $2$ .

$\frac{12 - 4 a \cdot 2 + a \cdot a}{2 a}$

Step 9.6

Multiply $2$ by $- 4$ .

$\frac{12 - 8 a + a \cdot a}{2 a}$

Step 9.7

Multiply $a$ by $a$ .

$\frac{12 - 8 a + a^{2}}{2 a}$

Step 9.8

Factor $12 - 8 a + a^{2}$ using the AC method.

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Step 9.8.1

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 $- 8$ .

$- 6, - 2$

Step 9.8.2

Write the factored form using these integers.

$\frac{(a - 6) (a - 2)}{2 a}$