Pre-Algebra Examples

$e = i r + i r$

Step 1

Rewrite the equation as $i r + i r = e$ .

$i r + i r = e$

Step 2

Add $i r$ and $i r$ .

$2 i r = e$

Step 3

Divide each term in $2 i r = e$ by $2 i$ and simplify.

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Step 3.1

Divide each term in $2 i r = e$ by $2 i$ .

$\frac{2 i r}{2 i} = \frac{e}{2 i}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 i r}{2 i} = \frac{e}{2 i}$

Step 3.2.1.2

Rewrite the expression.

$\frac{i r}{i} = \frac{e}{2 i}$

Step 3.2.2

Cancel the common factor of $i$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{i r}{i} = \frac{e}{2 i}$

Step 3.2.2.2

Divide $r$ by $1$ .

$r = \frac{e}{2 i}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator and denominator of $\frac{e}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

$r = \frac{e}{2 i} \cdot \frac{i}{i}$

Step 3.3.2

Multiply.

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Step 3.3.2.1

Combine.

$r = \frac{e i}{2 i i}$

Step 3.3.2.2

Simplify the denominator.

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Step 3.3.2.2.1

Add parentheses.

$r = \frac{e i}{2 (i i)}$

Step 3.3.2.2.2

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

$r = \frac{e i}{2 (i^{1} i)}$

Step 3.3.2.2.3

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

$r = \frac{e i}{2 (i^{1} i^{1})}$

Step 3.3.2.2.4

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

$r = \frac{e i}{2 i^{1 + 1}}$

Step 3.3.2.2.5

Add $1$ and $1$ .

$r = \frac{e i}{2 i^{2}}$

Step 3.3.2.2.6

Rewrite $i^{2}$ as $- 1$ .

$r = \frac{e i}{2 \cdot - 1}$

Step 3.3.3

Multiply $2$ by $- 1$ .

$r = \frac{e i}{- 2}$

Step 3.3.4

Move the negative in front of the fraction.

$r = - \frac{e i}{2}$