Step-by-Step Solution
Key Concept: $\\dfrac{(x - 7) - (x + 4)}{(x + 4)(x - 7)} = \\dfrac{11}{30} \Rightarrow \\dfrac{-11}{x^2 - 3x - 28} = \\dfrac{11}{30} \Rightarrow x^2 - 3x - 28 = -30 \Rightarrow x^2 - 3x + 2 = 0 \Rightarrow (x - 1)(x - 2) = 0 \Rightarrow x = 1$ or $x = 2$.
$\\dfrac{-11}{x^2 - 3x - 28} = \\dfrac{11}{30} \Rightarrow x^2 - 3x - 28 = -30$. [1.0 Mark]
$x^2 - 3x + 2 = 0 \Rightarrow (x - 1)(x - 2) = 0$. [1.0 Mark]
$x = 1$ or $x = 2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Simplifying fraction to $x^2 - 3x + 2 = 0$: 1.0 Mark
Factoring into $(x - 1)(x - 2) = 0$: 1.0 Mark
Finding roots $x = 1, x = 2$: 1.0 Mark
Correct Answer: