Solve 1/f=-1/4-1/2

$$\frac { 1 } { f } = \frac { - 1 } { 4 } - \frac { 1 } { 2 }$$

Solve for f

$$f = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4f, the least common multiple of f,4,2.

$$4=f\left(-1\right)+4f\left(-\frac{1}{2}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$4=f\left(-1\right)+\frac{4\left(-1\right)}{2}f$$

Multiply 4 and -1 to get -4.

$$4=f\left(-1\right)+\frac{-4}{2}f$$

Divide -4 by 2 to get -2.

$$4=f\left(-1\right)-2f$$

Combine f\left(-1\right) and -2f to get -3f.

$$4=-3f$$

Swap sides so that all variable terms are on the left hand side.

$$-3f=4$$

Divide both sides by -3.

$$f=\frac{4}{-3}$$

Fraction \frac{4}{-3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$f=-\frac{4}{3}$$