Pre-Algebra Examples

$a^{2} x = a (x + 2) - 2$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a^{2} x = a x + a \cdot 2 - 2$

Step 1.2

Move $2$ to the left of $a$ .

$a^{2} x = a x + 2 a - 2$

Step 2

Subtract $a x$ from both sides of the equation.

$a^{2} x - a x = 2 a - 2$

Step 3

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

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Step 3.1

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

$a x (a) - a x = 2 a - 2$

Step 3.2

Factor $a x$ out of $- a x$ .

$a x (a) + a x (- 1) = 2 a - 2$

Step 3.3

Factor $a x$ out of $a x (a) + a x (- 1)$ .

$a x (a - 1) = 2 a - 2$

Step 4

Divide each term in $a x (a - 1) = 2 a - 2$ by $a (a - 1)$ and simplify.

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Step 4.1

Divide each term in $a x (a - 1) = 2 a - 2$ by $a (a - 1)$ .

$\frac{a x (a - 1)}{a (a - 1)} = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $a$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{a x (a - 1)}{a (a - 1)} = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x (a - 1)}{a - 1} = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.2.2

Cancel the common factor of $a - 1$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x (a - 1)}{a - 1} = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $a$ .

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Step 4.3.1.1.1

Cancel the common factor.

$x = \frac{2 a}{a (a - 1)} + \frac{- 2}{a (a - 1)}$

Step 4.3.1.1.2

Rewrite the expression.

$x = \frac{2}{a - 1} + \frac{- 2}{a (a - 1)}$

Step 4.3.1.2

Move the negative in front of the fraction.

$x = \frac{2}{a - 1} - \frac{2}{a (a - 1)}$

Step 4.3.2

To write $\frac{2}{a - 1}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$x = \frac{2}{a - 1} \cdot \frac{a}{a} - \frac{2}{a (a - 1)}$

Step 4.3.3

Write each expression with a common denominator of $(a - 1) a$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.3.1

Multiply $\frac{2}{a - 1}$ by $\frac{a}{a}$ .

$x = \frac{2 a}{(a - 1) a} - \frac{2}{a (a - 1)}$

Step 4.3.3.2

Reorder the factors of $(a - 1) a$ .

$x = \frac{2 a}{a (a - 1)} - \frac{2}{a (a - 1)}$

Step 4.3.4

Combine the numerators over the common denominator.

$x = \frac{2 a - 2}{a (a - 1)}$

Step 4.3.5

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

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Step 4.3.5.1

Factor $2$ out of $2 a$ .

$x = \frac{2 (a) - 2}{a (a - 1)}$

Step 4.3.5.2

Factor $2$ out of $- 2$ .

$x = \frac{2 (a) + 2 (- 1)}{a (a - 1)}$

Step 4.3.5.3

Factor $2$ out of $2 (a) + 2 (- 1)$ .

$x = \frac{2 (a - 1)}{a (a - 1)}$

Step 4.3.6

Cancel the common factor of $a - 1$ .

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Step 4.3.6.1

Cancel the common factor.

$x = \frac{2 (a - 1)}{a (a - 1)}$

Step 4.3.6.2

Rewrite the expression.

$x = \frac{2}{a}$