Finite Math Examples

$\frac{3}{x - 2} + \frac{4}{5} = \frac{27}{5 (x - 2)}$

Step 1

Subtract $\frac{27}{5 (x - 2)}$ from both sides of the equation.

$\frac{3}{x - 2} + \frac{4}{5} - \frac{27}{5 (x - 2)} = 0$

Step 2

Simplify $\frac{3}{x - 2} + \frac{4}{5} - \frac{27}{5 (x - 2)}$ .

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Step 2.1

To write $\frac{3}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{x - 2} \cdot \frac{5}{5} + \frac{4}{5} - \frac{27}{5 (x - 2)} = 0$

Step 2.2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

$\frac{3}{x - 2} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{x - 2}{x - 2} - \frac{27}{5 (x - 2)} = 0$

Step 2.3

Write each expression with a common denominator of $(x - 2) \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{3}{x - 2}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 5}{(x - 2) \cdot 5} + \frac{4}{5} \cdot \frac{x - 2}{x - 2} - \frac{27}{5 (x - 2)} = 0$

Step 2.3.2

Multiply $\frac{4}{5}$ by $\frac{x - 2}{x - 2}$ .

$\frac{3 \cdot 5}{(x - 2) \cdot 5} + \frac{4 (x - 2)}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.3.3

Reorder the factors of $(x - 2) \cdot 5$ .

$\frac{3 \cdot 5}{5 (x - 2)} + \frac{4 (x - 2)}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 + 4 (x - 2)}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.5

Multiply $3$ by $5$ .

$\frac{15 + 4 (x - 2)}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Apply the distributive property.

$\frac{15 + 4 x + 4 \cdot - 2}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.6.2

Multiply $4$ by $- 2$ .

$\frac{15 + 4 x - 8}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.6.3

Subtract $8$ from $15$ .

$\frac{4 x + 7}{5 (x - 2)} - \frac{27}{5 (x - 2)} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{4 x + 7 - 27}{5 (x - 2)} = 0$

Step 2.8

Subtract $27$ from $7$ .

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

Step 2.9

Factor $4$ out of $4 x - 20$ .

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Step 2.9.1

Factor $4$ out of $4 x$ .

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

Step 2.9.2

Factor $4$ out of $- 20$ .

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

Step 2.9.3

Factor $4$ out of $4 x + 4 \cdot - 5$ .

$\frac{4 (x - 5)}{5 (x - 2)} = 0$

Step 3

Set the numerator equal to zero.

$4 (x - 5) = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Divide each term in $4 (x - 5) = 0$ by $4$ and simplify.

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Step 4.1.1

Divide each term in $4 (x - 5) = 0$ by $4$ .

$\frac{4 (x - 5)}{4} = \frac{0}{4}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $4$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{4 (x - 5)}{4} = \frac{0}{4}$

Step 4.1.2.1.2

Divide $x - 5$ by $1$ .

$x - 5 = \frac{0}{4}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $4$ .

$x - 5 = 0$

Step 4.2

Add $5$ to both sides of the equation.

$x = 5$