Algebra Examples

$p = i v$

Step 1

Rewrite the equation as $i v = p$ .

$i v = p$

Step 2

Divide each term in $i v = p$ by $i$ and simplify.

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Step 2.1

Divide each term in $i v = p$ by $i$ .

$\frac{i v}{i} = \frac{p}{i}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $i$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{i v}{i} = \frac{p}{i}$

Step 2.2.1.2

Divide $v$ by $1$ .

$v = \frac{p}{i}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$v = \frac{p}{i} \cdot \frac{i}{i}$

Step 2.3.2

Multiply.

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Step 2.3.2.1

Combine.

$v = \frac{p i}{i i}$

Step 2.3.2.2

Simplify the denominator.

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Step 2.3.2.2.1

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

$v = \frac{p i}{i^{1} i}$

Step 2.3.2.2.2

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

$v = \frac{p i}{i^{1} i^{1}}$

Step 2.3.2.2.3

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

$v = \frac{p i}{i^{1 + 1}}$

Step 2.3.2.2.4

Add $1$ and $1$ .

$v = \frac{p i}{i^{2}}$

Step 2.3.2.2.5

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

$v = \frac{p i}{- 1}$

Step 2.3.3

Move the negative one from the denominator of $\frac{p i}{- 1}$ .

$v = - 1 \cdot (p i)$

Step 2.3.4

Rewrite $- 1 \cdot (p i)$ as $- (p i)$ .

$v = - p i$