Basic Math Examples

$1 - 3 \div a a = 4$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$1 - \frac{3}{a \cdot a} = 4$

Step 1.2

Multiply $a$ by $a$ .

$1 - \frac{3}{a^{2}} = 4$

Step 2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.1

Subtract $1$ from both sides of the equation.

$- \frac{3}{a^{2}} = 4 - 1$

Step 2.2

Subtract $1$ from $4$ .

$- \frac{3}{a^{2}} = 3$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a^{2}, 1$

Step 3.2

The LCM of one and any expression is the expression.

$a^{2}$

Step 4

Multiply each term in $- \frac{3}{a^{2}} = 3$ by $a^{2}$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- \frac{3}{a^{2}} = 3$ by $a^{2}$ .

$- \frac{3}{a^{2}} a^{2} = 3 a^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Move the leading negative in $- \frac{3}{a^{2}}$ into the numerator.

$\frac{- 3}{a^{2}} a^{2} = 3 a^{2}$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 3}{a^{2}} a^{2} = 3 a^{2}$

Step 4.2.1.3

Rewrite the expression.

$- 3 = 3 a^{2}$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $3 a^{2} = - 3$ .

$3 a^{2} = - 3$

Step 5.2

Divide each term in $3 a^{2} = - 3$ by $3$ and simplify.

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Step 5.2.1

Divide each term in $3 a^{2} = - 3$ by $3$ .

$\frac{3 a^{2}}{3} = \frac{- 3}{3}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $3$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{3 a^{2}}{3} = \frac{- 3}{3}$

Step 5.2.2.1.2

Divide $a^{2}$ by $1$ .

$a^{2} = \frac{- 3}{3}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 3$ by $3$ .

$a^{2} = - 1$

Step 5.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{- 1}$

Step 5.4

Rewrite $\sqrt{- 1}$ as $i$ .

$a = \pm i$

Step 5.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.5.1

First, use the positive value of the $\pm$ to find the first solution.

$a = i$

Step 5.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$a = - i$

Step 5.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$a = i, - i$