Algebra Examples

$i = \frac{n e}{r + n r}$

Step 1

Rewrite the equation as $\frac{n e}{r + n r} = i$ .

$\frac{n e}{r + n r} = i$

Step 2

Factor $r$ out of $r + n r$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Factor $r$ out of $r^{1}$ .

$\frac{n e}{r \cdot 1 + n r} = i$

Step 2.3

Factor $r$ out of $n r$ .

$\frac{n e}{r \cdot 1 + r n} = i$

Step 2.4

Factor $r$ out of $r \cdot 1 + r n$ .

$\frac{n e}{r \cdot (1 + n)} = i$

Step 2.5

Multiply $r$ by $1 + n$ .

$\frac{n e}{r (1 + n)} = i$

Step 3

Find the LCD of the terms in the equation.

Tap for more steps...

Step 3.1

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

$r (1 + n), 1$

Step 3.2

The LCM of one and any expression is the expression.

$r (1 + n)$

Step 4

Multiply each term in $\frac{n e}{r (1 + n)} = i$ by $r (1 + n)$ to eliminate the fractions.

Tap for more steps...

Step 4.1

Multiply each term in $\frac{n e}{r (1 + n)} = i$ by $r (1 + n)$ .

$\frac{n e}{r (1 + n)} (r (1 + n)) = i (r (1 + n))$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $r (1 + n)$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{n e}{r (1 + n)} (r (1 + n)) = i (r (1 + n))$

Step 4.2.1.2

Rewrite the expression.

$n e = i (r (1 + n))$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Apply the distributive property.

$n e = i (r \cdot 1 + r n)$

Step 4.3.2

Multiply $r$ by $1$ .

$n e = i (r + r n)$

Step 4.3.3

Apply the distributive property.

$n e = i r + i r n$

Step 5

Solve the equation.

Tap for more steps...

Step 5.1

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

$i r + i r n = n e$

Step 5.2

Factor $i r$ out of $i r + i r n$ .

Tap for more steps...

Step 5.2.1

Factor $i r$ out of $i r$ .

$i r (1) + i r n = n e$

Step 5.2.2

Factor $i r$ out of $i r n$ .

$i r (1) + i r (n) = n e$

Step 5.2.3

Factor $i r$ out of $i r (1) + i r (n)$ .

$i r (1 + n) = n e$

Step 5.3

Divide each term in $i r (1 + n) = n e$ by $i (1 + n)$ and simplify.

Tap for more steps...

Step 5.3.1

Divide each term in $i r (1 + n) = n e$ by $i (1 + n)$ .

$\frac{i r (1 + n)}{i (1 + n)} = \frac{n e}{i (1 + n)}$

Step 5.3.2

Simplify the left side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of $i$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

$\frac{i r (1 + n)}{i (1 + n)} = \frac{n e}{i (1 + n)}$

Step 5.3.2.1.2

Rewrite the expression.

$\frac{r (1 + n)}{1 + n} = \frac{n e}{i (1 + n)}$

Step 5.3.2.2

Cancel the common factor of $1 + n$ .

Tap for more steps...

Step 5.3.2.2.1

Cancel the common factor.

$\frac{r (1 + n)}{1 + n} = \frac{n e}{i (1 + n)}$

Step 5.3.2.2.2

Divide $r$ by $1$ .

$r = \frac{n e}{i (1 + n)}$