Solve for $x$: $\frac{1}{x + 4} - \frac{1}{x + 7} = \frac{11}{30}$, $x
eq -4, 7$.

Question

Solve for $x$: $\frac{1}{x + 4} - \frac{1}{x + 7} = \frac{11}{30}$, $x 
eq -4, 7$.

Accepted Answer

Step 1: $\frac{1}{x + 4} - \frac{1}{x + 7} = \frac{11}{30} \Rightarrow \frac{x + 7 - x - 4}{(x + 4)(x + 7)} = \frac{11}{30}$
Step 2: $\Rightarrow x^2 - 3x + 2 = 0$
Step 3: $\Rightarrow (x - 2)(x - 1) = 0 \Rightarrow x = 2, 1$
Step 4: Alternative method: $\frac{1}{x + 4} + \frac{1}{x + 7} = \frac{11}{30}$ leading to $11x^2 + 121x + 218 = 0$. $D = 5049$. $x = \frac{-121 \pm \sqrt{5049}}{22}$

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