Solve by Factoring 2/(x+2)-1/x=-4/(x(x+2))

$\frac{2}{x + 2} - \frac{1}{x} = \frac{- 4}{x (x + 2)}$

Step 1

Subtract $\frac{- 4}{x (x + 2)}$ from both sides of the equation.

$\frac{2}{x + 2} - \frac{1}{x} - \frac{- 4}{x (x + 2)} = 0$

Step 2

Simplify $\frac{2}{x + 2} - \frac{1}{x} - \frac{- 4}{x (x + 2)}$ .

Simplify each term.

Move the negative in front of the fraction.

$\frac{2}{x + 2} - \frac{1}{x} - - \frac{4}{x (x + 2)} = 0$

Multiply $- - \frac{4}{x (x + 2)}$ .

Multiply $- 1$ by $- 1$ .

$\frac{2}{x + 2} - \frac{1}{x} + 1 \frac{4}{x (x + 2)} = 0$

Multiply $\frac{4}{x (x + 2)}$ by $1$ .

$\frac{2}{x + 2} - \frac{1}{x} + \frac{4}{x (x + 2)} = 0$

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

$\frac{2}{x + 2} \cdot \frac{x}{x} - \frac{1}{x} + \frac{4}{x (x + 2)} = 0$

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{2}{x + 2} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{x + 2}{x + 2} + \frac{4}{x (x + 2)} = 0$

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

Multiply $\frac{2}{x + 2}$ by $\frac{x}{x}$ .

$\frac{2 x}{(x + 2) x} - \frac{1}{x} \cdot \frac{x + 2}{x + 2} + \frac{4}{x (x + 2)} = 0$

Multiply $\frac{1}{x}$ by $\frac{x + 2}{x + 2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

$\frac{2 x - x - 1 \cdot 2}{x (x + 2)} + \frac{4}{x (x + 2)} = 0$

Multiply $- 1$ by $2$ .

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

Subtract $x$ from $2 x$ .

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

Combine the numerators over the common denominator.

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

Add $- 2$ and $4$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x} = 0$

Step 3

Set the numerator equal to zero.

$1 = 0$

Step 4

Since $1 \neq 0$ , there are no solutions.

No solution

Solve by Factoring 2/(x+2)-1/x=-4/(x(x+2))

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