Solve 1/60=1/133hbar+1/F_{1}

$$\frac { 1 } { 60 } = \frac { 1 } { 133 \hbar } + \frac { 1 } { F _ { 1 } }$$

Solve for F_1

$$F_{1}=-\frac{7980ℏ}{60-133ℏ}$$

$$ℏ\neq 0\text{ and }ℏ\neq \frac{60}{133}$$

Steps for Solving Linear Equation

Variable F_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7980F_{1}ℏ, the least common multiple of 60,133ℏ,F_{1}.

$$133F_{1}ℏ=60F_{1}+7980ℏ$$

Subtract 60F_{1} from both sides.

$$133F_{1}ℏ-60F_{1}=7980ℏ$$

Combine all terms containing F_{1}.

$$\left(133ℏ-60\right)F_{1}=7980ℏ$$

Divide both sides by 133ℏ-60.

$$\frac{\left(133ℏ-60\right)F_{1}}{133ℏ-60}=\frac{7980ℏ}{133ℏ-60}$$

Dividing by 133ℏ-60 undoes the multiplication by 133ℏ-60.

$$F_{1}=\frac{7980ℏ}{133ℏ-60}$$

Variable F_{1} cannot be equal to 0.

$$F_{1}=\frac{7980ℏ}{133ℏ-60}\text{, }F_{1}\neq 0$$

Solve for ℏ

$$ℏ=-\frac{60F_{1}}{133\left(60-F_{1}\right)}$$

$$F_{1}\neq 0\text{ and }F_{1}\neq 60$$

Steps for Solving Linear Equation

Variable ℏ cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7980F_{1}ℏ, the least common multiple of 60,133ℏ,F_{1}.

$$133F_{1}ℏ=60F_{1}+7980ℏ$$

Subtract 7980ℏ from both sides.

$$133F_{1}ℏ-7980ℏ=60F_{1}$$

Combine all terms containing ℏ.

$$\left(133F_{1}-7980\right)ℏ=60F_{1}$$

Divide both sides by 133F_{1}-7980.

$$\frac{\left(133F_{1}-7980\right)ℏ}{133F_{1}-7980}=\frac{60F_{1}}{133F_{1}-7980}$$

Dividing by 133F_{1}-7980 undoes the multiplication by 133F_{1}-7980.

$$ℏ=\frac{60F_{1}}{133F_{1}-7980}$$

Divide 60F_{1} by 133F_{1}-7980.

$$ℏ=\frac{60F_{1}}{133\left(F_{1}-60\right)}$$

Variable ℏ cannot be equal to 0.

$$ℏ=\frac{60F_{1}}{133\left(F_{1}-60\right)}\text{, }ℏ\neq 0$$