Find the Roots (Zeros) f(x)=-4/x+1

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

Set $\frac{- 4}{x} + 1$ equal to $0$ .

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

Solve for $x$ .

Subtract $1$ from both sides of the equation.

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

Move the negative in front of the fraction.

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

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $- \frac{4}{x} = - 1$ by $x$ to eliminate the fractions.

Multiply each term in $- \frac{4}{x} = - 1$ by $x$ .

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

Simplify the left side.

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{4}{x}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 4 = - x$

Solve the equation.

Rewrite the equation as $- x = - 4$ .

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$