Question

1. what is the solution of $\frac{3}{2} - \frac{1}{f} = \frac{f - 2}{3}$?

• $\frac{1}{2}$ or 6
• no solution
• 2 or 6
• $\frac{1}{2}$ only

Explanation:

Step1: Find common denominator

Multiply both sides by $6f$: $6f(\frac{3}{2}) - 6f(\frac{1}{f}) = 6f(\frac{f-2}{3})$

Step2: Simplify each term

$9f - 6 = 2f(f - 2)$

Step3: Expand right side

$9f - 6 = 2f^2 - 4f$

Step4: Rearrange to quadratic equation

$2f^2 - 13f + 6 = 0$

Step5: Solve quadratic equation

Factor: $(2f - 1)(f - 6) = 0$, so $f=\frac{1}{2}$ or $f=6$

Answer:

$\frac{1}{2}$ or 6