Finite Math Examples

$\frac{5 x - 3}{15} = \frac{x + 5}{3} - \frac{x - 2}{15}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{x + 5}{3}$ from both sides of the equation.

$\frac{5 x - 3}{15} - \frac{x + 5}{3} = - \frac{x - 2}{15}$

Step 1.2

Add $\frac{x - 2}{15}$ to both sides of the equation.

$\frac{5 x - 3}{15} - \frac{x + 5}{3} + \frac{x - 2}{15} = 0$

Step 2

Simplify $\frac{5 x - 3}{15} - \frac{x + 5}{3} + \frac{x - 2}{15}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 x - 3 + x - 2}{15} + \frac{- (x + 5)}{3} = 0$

Step 2.2

Add $5 x$ and $x$ .

$\frac{6 x - 3 - 2}{15} + \frac{- (x + 5)}{3} = 0$

Step 2.3

Subtract $2$ from $- 3$ .

$\frac{6 x - 5}{15} + \frac{- (x + 5)}{3} = 0$

Step 2.4

Move the negative in front of the fraction.

$\frac{6 x - 5}{15} - \frac{x + 5}{3} = 0$

Step 2.5

To write $- \frac{x + 5}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 x - 5}{15} - \frac{x + 5}{3} \cdot \frac{5}{5} = 0$

Step 2.6

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{x + 5}{3}$ by $\frac{5}{5}$ .

$\frac{6 x - 5}{15} - \frac{(x + 5) \cdot 5}{3 \cdot 5} = 0$

Step 2.6.2

Multiply $3$ by $5$ .

$\frac{6 x - 5}{15} - \frac{(x + 5) \cdot 5}{15} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{6 x - 5 - (x + 5) \cdot 5}{15} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Apply the distributive property.

$\frac{6 x - 5 + (- x - 1 \cdot 5) \cdot 5}{15} = 0$

Step 2.8.2

Multiply $- 1$ by $5$ .

$\frac{6 x - 5 + (- x - 5) \cdot 5}{15} = 0$

Step 2.8.3

Apply the distributive property.

$\frac{6 x - 5 - x \cdot 5 - 5 \cdot 5}{15} = 0$

Step 2.8.4

Multiply $5$ by $- 1$ .

$\frac{6 x - 5 - 5 x - 5 \cdot 5}{15} = 0$

Step 2.8.5

Multiply $- 5$ by $5$ .

$\frac{6 x - 5 - 5 x - 25}{15} = 0$

Step 2.8.6

Subtract $5 x$ from $6 x$ .

$\frac{x - 5 - 25}{15} = 0$

Step 2.8.7

Subtract $25$ from $- 5$ .

$\frac{x - 30}{15} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.