Solve by Factoring 1/x-x/4=0

$\frac{1}{x} - \frac{x}{4} = 0$

Step 1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{x} \cdot \frac{4}{4} - \frac{x}{4} = 0$

Step 2

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

$\frac{1}{x} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{x}{x} = 0$

Step 3

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x}$ by $\frac{4}{4}$ .

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

Multiply $\frac{x}{4}$ by $\frac{x}{x}$ .

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

Reorder the factors of $x \cdot 4$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{2^{2} - x \cdot x}{4 x} = 0$

Rewrite $x \cdot x$ as $x^{2}$ .

$\frac{2^{2} - x^{2}}{4 x} = 0$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

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

Step 6

Set the numerator equal to zero.

$(2 + x) (2 - x) = 0$

Step 7

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 + x = 0$

$2 - x = 0$

Set $2 + x$ equal to $0$ and solve for $x$ .

Set $2 + x$ equal to $0$ .

$2 + x = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $2 - x$ equal to $0$ and solve for $x$ .

Set $2 - x$ equal to $0$ .

$2 - x = 0$

Solve $2 - x = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

The final solution is all the values that make $(2 + x) (2 - x) = 0$ true.

$x = - 2, 2$

Solve by Factoring 1/x-x/4=0

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