Finite Math Examples

$\frac{3 x + 3}{x - 3} = 9$

Step 1

Subtract $9$ from both sides of the equation.

$\frac{3 x + 3}{x - 3} - 9 = 0$

Step 2

Simplify $\frac{3 x + 3}{x - 3} - 9$ .

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Step 2.1

Factor $3$ out of $3 x + 3$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 3}{x - 3} - 9 = 0$

Step 2.1.2

Factor $3$ out of $3$ .

$\frac{3 (x) + 3 (1)}{x - 3} - 9 = 0$

Step 2.1.3

Factor $3$ out of $3 (x) + 3 (1)$ .

$\frac{3 (x + 1)}{x - 3} - 9 = 0$

Step 2.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{3 (x + 1)}{x - 3} - 9 \cdot \frac{x - 3}{x - 3} = 0$

Step 2.3

Combine $- 9$ and $\frac{x - 3}{x - 3}$ .

$\frac{3 (x + 1)}{x - 3} + \frac{- 9 (x - 3)}{x - 3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 (x + 1) - 9 (x - 3)}{x - 3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $3$ out of $3 (x + 1) - 9 (x - 3)$ .

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Step 2.5.1.1

Factor $3$ out of $- 9 (x - 3)$ .

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

Step 2.5.1.2

Factor $3$ out of $3 (x + 1) + 3 (- 3 (x - 3))$ .

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

Step 2.5.2

Apply the distributive property.

$\frac{3 (x + 1 - 3 x - 3 \cdot - 3)}{x - 3} = 0$

Step 2.5.3

Multiply $- 3$ by $- 3$ .

$\frac{3 (x + 1 - 3 x + 9)}{x - 3} = 0$

Step 2.5.4

Subtract $3 x$ from $x$ .

$\frac{3 (- 2 x + 1 + 9)}{x - 3} = 0$

Step 2.5.5

Add $1$ and $9$ .

$\frac{3 (- 2 x + 10)}{x - 3} = 0$

Step 2.5.6

Factor $2$ out of $- 2 x + 10$ .

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Step 2.5.6.1

Factor $2$ out of $- 2 x$ .

$\frac{3 (2 (- x) + 10)}{x - 3} = 0$

Step 2.5.6.2

Factor $2$ out of $10$ .

$\frac{3 (2 (- x) + 2 (5))}{x - 3} = 0$

Step 2.5.6.3

Factor $2$ out of $2 (- x) + 2 (5)$ .

$\frac{3 (2 (- x + 5))}{x - 3} = 0$

$\frac{3 \cdot 2 (- x + 5)}{x - 3} = 0$

Step 2.5.7

Multiply $3$ by $2$ .

$\frac{6 (- x + 5)}{x - 3} = 0$

Step 2.6

Factor $- 1$ out of $- x$ .

$\frac{6 (- (x) + 5)}{x - 3} = 0$

Step 2.7

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{6 (- (x) - 1 (- 5))}{x - 3} = 0$

Step 2.8

Factor $- 1$ out of $- (x) - 1 (- 5)$ .

$\frac{6 (- (x - 5))}{x - 3} = 0$

Step 2.9

Rewrite $- (x - 5)$ as $- 1 (x - 5)$ .

$\frac{6 (- 1 (x - 5))}{x - 3} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{6 (x - 5)}{x - 3} = 0$