How to solve 1/f = 1/u + 1/v

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 1/f = 1/u + 1/v | Equatix

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Question

$$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$$

Solve for f

$f=\frac{uv}{u+v}$
$v\neq 0\text{ and }u\neq 0\text{ and }u\neq -v$

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 $fuv$, the least common multiple of $f,u,v$.

$$uv=fv+fu$$

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

$$fv+fu=uv$$

Combine all terms containing $f$.

$$\left(v+u\right)f=uv$$

The equation is in standard form.

$$\left(u+v\right)f=uv$$

Divide both sides by $v+u$.

$$\frac{\left(u+v\right)f}{u+v}=\frac{uv}{u+v}$$

Dividing by $v+u$ undoes the multiplication by $v+u$.

$$f=\frac{uv}{u+v}$$

Variable $f$ cannot be equal to $0$.

$$f=\frac{uv}{u+v}\text{, }f\neq 0$$

Show Solution

Solve for u

$u=-\frac{fv}{f-v}$
$v\neq 0\text{ and }f\neq 0\text{ and }f\neq v$

Steps for Solving Linear Equation

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

$$uv=fv+fu$$

Subtract $fu$ from both sides.

$$uv-fu=fv$$

Combine all terms containing $u$.

$$\left(v-f\right)u=fv$$

Divide both sides by $v-f$.

$$\frac{\left(v-f\right)u}{v-f}=\frac{fv}{v-f}$$

Dividing by $v-f$ undoes the multiplication by $v-f$.

$$u=\frac{fv}{v-f}$$

Variable $u$ cannot be equal to $0$.

$$u=\frac{fv}{v-f}\text{, }u\neq 0$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for f

Steps for Solving Linear Equation

Solve for u

Steps for Solving Linear Equation