Algebra Examples

$\frac{3}{x - 2} + \frac{7}{x} = \frac{- 14}{x^{2} - 2 x}$

Step 1

Subtract $\frac{- 14}{x^{2} - 2 x}$ from both sides of the equation.

$\frac{3}{x - 2} + \frac{7}{x} - \frac{- 14}{x^{2} - 2 x} = 0$

Step 2

Simplify $\frac{3}{x - 2} + \frac{7}{x} - \frac{- 14}{x^{2} - 2 x}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Factor $x$ out of $x^{2} - 2 x$ .

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Step 2.1.1.1

Factor $x$ out of $x^{2}$ .

$\frac{3}{x - 2} + \frac{7}{x} - \frac{- 14}{x \cdot x - 2 x} = 0$

Step 2.1.1.2

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

$\frac{3}{x - 2} + \frac{7}{x} - \frac{- 14}{x \cdot x + x \cdot - 2} = 0$

Step 2.1.1.3

Factor $x$ out of $x \cdot x + x \cdot - 2$ .

$\frac{3}{x - 2} + \frac{7}{x} - \frac{- 14}{x (x - 2)} = 0$

Step 2.1.2

Move the negative in front of the fraction.

$\frac{3}{x - 2} + \frac{7}{x} - - \frac{14}{x (x - 2)} = 0$

Step 2.1.3

Multiply $- - \frac{14}{x (x - 2)}$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{3}{x - 2} + \frac{7}{x} + 1 \frac{14}{x (x - 2)} = 0$

Step 2.1.3.2

Multiply $\frac{14}{x (x - 2)}$ by $1$ .

$\frac{3}{x - 2} + \frac{7}{x} + \frac{14}{x (x - 2)} = 0$

Step 2.2

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

$\frac{3}{x - 2} \cdot \frac{x}{x} + \frac{7}{x} + \frac{14}{x (x - 2)} = 0$

Step 2.3

To write $\frac{7}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

$\frac{3}{x - 2} \cdot \frac{x}{x} + \frac{7}{x} \cdot \frac{x - 2}{x - 2} + \frac{14}{x (x - 2)} = 0$

Step 2.4

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

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Step 2.4.1

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

$\frac{3 x}{(x - 2) x} + \frac{7}{x} \cdot \frac{x - 2}{x - 2} + \frac{14}{x (x - 2)} = 0$

Step 2.4.2

Multiply $\frac{7}{x}$ by $\frac{x - 2}{x - 2}$ .

$\frac{3 x}{(x - 2) x} + \frac{7 (x - 2)}{x (x - 2)} + \frac{14}{x (x - 2)} = 0$

Step 2.4.3

Reorder the factors of $(x - 2) x$ .

$\frac{3 x}{x (x - 2)} + \frac{7 (x - 2)}{x (x - 2)} + \frac{14}{x (x - 2)} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{3 x + 7 (x - 2)}{x (x - 2)} + \frac{14}{x (x - 2)} = 0$

Step 2.6

Combine the numerators over the common denominator.

$\frac{3 x + 7 (x - 2) + 14}{x (x - 2)} = 0$

Step 2.7

Simplify each term.

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Step 2.7.1

Apply the distributive property.

$\frac{3 x + 7 x + 7 \cdot - 2 + 14}{x (x - 2)} = 0$

Step 2.7.2

Multiply $7$ by $- 2$ .

$\frac{3 x + 7 x - 14 + 14}{x (x - 2)} = 0$

Step 2.8

Combine the opposite terms in $3 x + 7 x - 14 + 14$ .

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Step 2.8.1

Add $- 14$ and $14$ .

$\frac{3 x + 7 x + 0}{x (x - 2)} = 0$

Step 2.8.2

Add $3 x + 7 x$ and $0$ .

$\frac{3 x + 7 x}{x (x - 2)} = 0$

Step 2.9

Add $3 x$ and $7 x$ .

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

Step 2.10

Cancel the common factor of $x$ .

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Step 2.10.1

Cancel the common factor.

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

Step 2.10.2

Rewrite the expression.

$\frac{10}{x - 2} = 0$

Step 3

Set the numerator equal to zero.

$10 = 0$

Step 4

Since $10 \neq 0$ , there are no solutions.

No solution