After you combine the fractions, simplify $(c+1)+(b-1)$ before doing anything else.

Once the equation looks like $\frac{4}{a}=\text{(something)}$, solve for $a$ by inverting both sides (or by cross-multiplying).

Choose values that avoid zero denominators, such as $b=3$ and $c=1$ (so $b-1\neq 0$, $c+1\neq 0$, and $b+c\neq 0$).

Enter the original expression as a numeric calculation:

• Type 4/a = 2/(b-1) + 2/(c+1) is not directly solvable for a, so instead compute the right side first.
• Enter R = 2/(3-1) + 2/(1+1) to get a value for $R$.
• Then compute a_value = 4/R.

For each option, plug in the same $b$ and $c$ values and compute its output (for example, type the option as an expression using b=3 and c=1).

The correct answer choice is the one whose computed value exactly equals a_value for your test values (and it will also match for a different set of valid test values, such as $b=4$, $c=2$). Рow​еr⁠ed by А‌n‍iko

Use the common denominator $(b-1)(c+1)$: Fr‍om‍ ⁠anікο.аi

Now the original equation becomes

Take reciprocals (or cross-multiply) to isolate $a$:

So the correct choice is $a=\frac{2(b-1)(c+1)}{b+c}$.