Algebra Examples

$\frac{n}{n - 3} + n = \frac{7 n - 18}{n - 3}$

Step 1

Subtract $\frac{7 n - 18}{n - 3}$ from both sides of the equation.

$\frac{n}{n - 3} + n - \frac{7 n - 18}{n - 3} = 0$

Step 2

Simplify $\frac{n}{n - 3} + n - \frac{7 n - 18}{n - 3}$ .

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Step 2.1

Combine the numerators over the common denominator.

$n + \frac{n - (7 n - 18)}{n - 3} = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$n + \frac{n - (7 n) - - 18}{n - 3} = 0$

Step 2.2.2

Multiply $7$ by $- 1$ .

$n + \frac{n - 7 n - - 18}{n - 3} = 0$

Step 2.2.3

Multiply $- 1$ by $- 18$ .

$n + \frac{n - 7 n + 18}{n - 3} = 0$

Step 2.3

Subtract $7 n$ from $n$ .

$n + \frac{- 6 n + 18}{n - 3} = 0$

Step 2.4

Simplify each term.

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Step 2.4.1

Factor $6$ out of $- 6 n + 18$ .

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Step 2.4.1.1

Factor $6$ out of $- 6 n$ .

$n + \frac{6 (- n) + 18}{n - 3} = 0$

Step 2.4.1.2

Factor $6$ out of $18$ .

$n + \frac{6 (- n) + 6 (3)}{n - 3} = 0$

Step 2.4.1.3

Factor $6$ out of $6 (- n) + 6 (3)$ .

$n + \frac{6 (- n + 3)}{n - 3} = 0$

Step 2.4.2

Cancel the common factor of $- n + 3$ and $n - 3$ .

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Step 2.4.2.1

Factor $- 1$ out of $- n$ .

$n + \frac{6 (- (n) + 3)}{n - 3} = 0$

Step 2.4.2.2

Rewrite $3$ as $- 1 (- 3)$ .

$n + \frac{6 (- (n) - 1 (- 3))}{n - 3} = 0$

Step 2.4.2.3

Factor $- 1$ out of $- (n) - 1 (- 3)$ .

$n + \frac{6 (- (n - 3))}{n - 3} = 0$

Step 2.4.2.4

Rewrite $- (n - 3)$ as $- 1 (n - 3)$ .

$n + \frac{6 (- 1 (n - 3))}{n - 3} = 0$

Step 2.4.2.5

Cancel the common factor.

$n + \frac{6 (- 1 (n - 3))}{n - 3} = 0$

Step 2.4.2.6

Divide $6 \cdot (- 1)$ by $1$ .

$n + 6 \cdot (- 1) = 0$

Step 2.4.3

Multiply $6$ by $- 1$ .

$n - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$n = 6$