Pre-Algebra Examples

$12 - x - x^{2} \div 5 x^{2} + 30 x + 40$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$12 - x - \frac{x^{2}}{5 x^{2}} + 30 x + 40$

Step 1.2

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

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Step 1.2.1

Cancel the common factor.

$12 - x - \frac{x^{2}}{5 x^{2}} + 30 x + 40$

Step 1.2.2

Rewrite the expression.

$12 - x - \frac{1}{5} + 30 x + 40$

Step 2

To write $12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x + 12 \cdot \frac{5}{5} - \frac{1}{5} + 30 x + 40$

Step 3

Combine $12$ and $\frac{5}{5}$ .

$- x + \frac{12 \cdot 5}{5} - \frac{1}{5} + 30 x + 40$

Step 4

Combine the numerators over the common denominator.

$- x + \frac{12 \cdot 5 - 1}{5} + 30 x + 40$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $12$ by $5$ .

$- x + \frac{60 - 1}{5} + 30 x + 40$

Step 5.2

Subtract $1$ from $60$ .

$- x + \frac{59}{5} + 30 x + 40$

Step 6

Add $- x$ and $30 x$ .

$29 x + \frac{59}{5} + 40$

Step 7

To write $40$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$29 x + \frac{59}{5} + 40 \cdot \frac{5}{5}$

Step 8

Combine $40$ and $\frac{5}{5}$ .

$29 x + \frac{59}{5} + \frac{40 \cdot 5}{5}$

Step 9

Combine the numerators over the common denominator.

$29 x + \frac{59 + 40 \cdot 5}{5}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $40$ by $5$ .

$29 x + \frac{59 + 200}{5}$

Step 10.2

Add $59$ and $200$ .

$29 x + \frac{259}{5}$