Finite Math Examples

$\frac{6}{5 (0) + 20} = \frac{4}{0 + 4} - \frac{2}{5}$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $\frac{4}{0 + 4}$ from both sides of the equation.

$\frac{6}{5 (0) + 20} - \frac{4}{0 + 4} = - \frac{2}{5}$

Step 1.2

Add $\frac{2}{5}$ to both sides of the equation.

$\frac{6}{5 (0) + 20} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2

Simplify $\frac{6}{5 (0) + 20} - \frac{4}{0 + 4} + \frac{2}{5}$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $6$ and $5 (0) + 20$ .

Tap for more steps...

Step 2.1.1.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{5 (0) + 20} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.1.2.1

Factor $2$ out of $5 (0)$ .

$\frac{2 (3)}{2 (5 \cdot (0)) + 20} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.1.2.2

Factor $2$ out of $20$ .

$\frac{2 \cdot 3}{2 (5 \cdot (0)) + 2 \cdot 10} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.1.2.3

Factor $2$ out of $2 (5 \cdot (0)) + 2 (10)$ .

$\frac{2 (3)}{2 (5 \cdot (0) + 10)} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{2 \cdot 3}{2 (5 \cdot (0) + 10)} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{3}{5 \cdot (0) + 10} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.2

Simplify the denominator.

Tap for more steps...

Step 2.1.2.1

Multiply $5$ by $0$ .

$\frac{3}{0 + 10} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.2.2

Add $0$ and $10$ .

$\frac{3}{10} - \frac{4}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.3

Cancel the common factor of $4$ and $0 + 4$ .

Tap for more steps...

Step 2.1.3.1

Factor $4$ out of $4$ .

$\frac{3}{10} - \frac{4 (1)}{0 + 4} + \frac{2}{5} = 0$

Step 2.1.3.2

Cancel the common factors.

Tap for more steps...

Step 2.1.3.2.1

Factor $4$ out of $0$ .

$\frac{3}{10} - \frac{4 \cdot 1}{4 \cdot 0 + 4} + \frac{2}{5} = 0$

Step 2.1.3.2.2

Factor $4$ out of $4$ .

$\frac{3}{10} - \frac{4 (1)}{4 \cdot 0 + 4 \cdot 1} + \frac{2}{5} = 0$

Step 2.1.3.2.3

Factor $4$ out of $4 \cdot 0 + 4 \cdot 1$ .

$\frac{3}{10} - \frac{4 (1)}{4 \cdot (0 + 1)} + \frac{2}{5} = 0$

Step 2.1.3.2.4

Cancel the common factor.

$\frac{3}{10} - \frac{4 \cdot 1}{4 \cdot (0 + 1)} + \frac{2}{5} = 0$

Step 2.1.3.2.5

Rewrite the expression.

$\frac{3}{10} - \frac{1}{0 + 1} + \frac{2}{5} = 0$

Step 2.1.4

Add $0$ and $1$ .

$\frac{3}{10} - \frac{1}{1} + \frac{2}{5} = 0$

Step 2.1.5

Cancel the common factor of $1$ .

Tap for more steps...

Step 2.1.5.1

Cancel the common factor.

$\frac{3}{10} - \frac{1}{1} + \frac{2}{5} = 0$

Step 2.1.5.2

Rewrite the expression.

$\frac{3}{10} - 1 \cdot 1 + \frac{2}{5} = 0$

Step 2.1.6

Multiply $- 1$ by $1$ .

$\frac{3}{10} - 1 + \frac{2}{5} = 0$

Step 2.2

Find the common denominator.

Tap for more steps...

Step 2.2.1

Write $- 1$ as a fraction with denominator $1$ .

$\frac{3}{10} + \frac{- 1}{1} + \frac{2}{5} = 0$

Step 2.2.2

Multiply $\frac{- 1}{1}$ by $\frac{10}{10}$ .

$\frac{3}{10} + \frac{- 1}{1} \cdot \frac{10}{10} + \frac{2}{5} = 0$

Step 2.2.3

Multiply $\frac{- 1}{1}$ by $\frac{10}{10}$ .

$\frac{3}{10} + \frac{- 1 \cdot 10}{10} + \frac{2}{5} = 0$

Step 2.2.4

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$\frac{3}{10} + \frac{- 1 \cdot 10}{10} + \frac{2}{5} \cdot \frac{2}{2} = 0$

Step 2.2.5

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$\frac{3}{10} + \frac{- 1 \cdot 10}{10} + \frac{2 \cdot 2}{5 \cdot 2} = 0$

Step 2.2.6

Reorder the factors of $5 \cdot 2$ .

$\frac{3}{10} + \frac{- 1 \cdot 10}{10} + \frac{2 \cdot 2}{2 \cdot 5} = 0$

Step 2.2.7

Multiply $2$ by $5$ .

$\frac{3}{10} + \frac{- 1 \cdot 10}{10} + \frac{2 \cdot 2}{10} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3 - 1 \cdot 10 + 2 \cdot 2}{10} = 0$

Step 2.4

Simplify each term.

Tap for more steps...

Step 2.4.1

Multiply $- 1$ by $10$ .

$\frac{3 - 10 + 2 \cdot 2}{10} = 0$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{3 - 10 + 4}{10} = 0$

Step 2.5

Subtract $10$ from $3$ .

$\frac{- 7 + 4}{10} = 0$

Step 2.6

Add $- 7$ and $4$ .

$\frac{- 3}{10} = 0$

Step 2.7

Move the negative in front of the fraction.

$- \frac{3}{10} = 0$

Step 3

Set the numerator equal to zero.

$3 = 0$

Step 4

Since $3 \neq 0$ , there are no solutions.

No solution