Solve by Factoring 1/x=5/(x-4)

$\frac{1}{x} = \frac{5}{x - 4}$

Step 1

Subtract $\frac{5}{x - 4}$ from both sides of the equation.

$\frac{1}{x} - \frac{5}{x - 4} = 0$

Step 2

Simplify $\frac{1}{x} - \frac{5}{x - 4}$ .

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

$\frac{1}{x} \cdot \frac{x - 4}{x - 4} - \frac{5}{x - 4} = 0$

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

$\frac{1}{x} \cdot \frac{x - 4}{x - 4} - \frac{5}{x - 4} \cdot \frac{x}{x} = 0$

Write each expression with a common denominator of $x (x - 4)$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $(x - 4) x$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Subtract $5 x$ from $x$ .

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

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

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

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

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $4 (- x) + 4 (- 1)$ .

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

Factor $- 1$ out of $- x$ .

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

Rewrite $- 1$ as $- 1 (1)$ .

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

Factor $- 1$ out of $- (x) - 1 (1)$ .

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

Rewrite $- (x + 1)$ as $- 1 (x + 1)$ .

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

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$4 (x + 1) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $4 (x + 1) = 0$ by $4$ and simplify.

Divide each term in $4 (x + 1) = 0$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x + 1$ by $1$ .

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

Simplify the right side.

Divide $0$ by $4$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Solve by Factoring 1/x=5/(x-4)

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