Algebra Examples

$(3 x^{2} + 12 x - 5) \div x + 5$

Step 1

Rewrite the division as a fraction.

$\frac{3 x^{2} + 12 x - 5}{x} + 5$

Step 2

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

$\frac{3 x^{2} + 12 x - 5}{x} + \frac{5 x}{x}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 x^{2} + 12 x - 5 + 5 x}{x}$

Step 4

Add $12 x$ and $5 x$ .

$\frac{3 x^{2} + 17 x - 5}{x}$

Step 5

Split the fraction $\frac{3 x^{2} + 17 x - 5}{x}$ into two fractions.

$\frac{3 x^{2} + 17 x}{x} + \frac{- 5}{x}$

Step 6

Split the fraction $\frac{3 x^{2} + 17 x}{x}$ into two fractions.

$\frac{3 x^{2}}{x} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7

Cancel the common factor of $x^{2}$ and $x$ .

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Step 7.1

Factor $x$ out of $3 x^{2}$ .

$\frac{x (3 x)}{x} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{x (3 x)}{x^{1}} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (3 x)}{x \cdot 1} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7.2.3

Cancel the common factor.

$\frac{x (3 x)}{x \cdot 1} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7.2.4

Rewrite the expression.

$\frac{3 x}{1} + \frac{17 x}{x} + \frac{- 5}{x}$

Step 7.2.5

Divide $3 x$ by $1$ .

$3 x + \frac{17 x}{x} + \frac{- 5}{x}$

Step 8

Cancel the common factor of $x$ .

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Step 8.1

Cancel the common factor.

$3 x + \frac{17 x}{x} + \frac{- 5}{x}$

Step 8.2

Divide $17$ by $1$ .

$3 x + 17 + \frac{- 5}{x}$

Step 9

Move the negative in front of the fraction.

$3 x + 17 - \frac{5}{x}$