Basic Math Examples

$(f + 2) \div f^{2} + 5 f + 6$

Step 1

To write $5 f$ as a fraction with a common denominator, multiply by $\frac{f^{2}}{f^{2}}$ .

$(f + 2) \div f^{2} + \frac{5 f \cdot f^{2}}{f^{2}} + 6$

Step 2

Combine the numerators over the common denominator.

$(f + 2 + 5 f \cdot f^{2}) \div f^{2} + 6$

Step 3

To write $6$ as a fraction with a common denominator, multiply by $\frac{f^{2}}{f^{2}}$ .

$(f + 2 + 5 f \cdot f^{2}) \div f^{2} + \frac{6 f^{2}}{f^{2}}$

Step 4

Combine the numerators over the common denominator.

$(f + 2 + 5 f \cdot f^{2} + 6 f^{2}) \div f^{2}$

Step 5

Reorder terms.

$(6 f^{2} + 5 f^{2} f + f + 2) \div f^{2}$

Step 6

Rewrite $(6 f^{2} + 5 f^{2} f + f + 2) \div f^{2}$ in a factored form.

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Step 6.1

Multiply $f^{2}$ by $f$ by adding the exponents.

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Step 6.1.1

Move $f$ .

$(6 f^{2} + 5 (f \cdot f^{2}) + f + 2) \div f^{2}$

Step 6.1.2

Multiply $f$ by $f^{2}$ .

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Step 6.1.2.1

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

$(6 f^{2} + 5 (f^{1} f^{2}) + f + 2) \div f^{2}$

Step 6.1.2.2

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

$(6 f^{2} + 5 f^{1 + 2} + f + 2) \div f^{2}$

Step 6.1.3

Add $1$ and $2$ .

$(6 f^{2} + 5 f^{3} + f + 2) \div f^{2}$

Step 6.2

Reorder terms.

$(5 f^{3} + 6 f^{2} + f + 2) \div f^{2}$