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TS EAMCET · Maths · Basic of Mathematics

\(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) is equal to

  1. A \((-1,4)\)
  2. B \((1,4) \cup(5,7)\)
  3. C \((1,7)\)
  4. D \((-1,1) \cup(4,6)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((-1,1) \cup(4,6)\)

Step-by-step Solution

Detailed explanation

\(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) \(\frac{14 x(x-4)-(9 x-30)(x+1)}{(x+1)(x-4)} < 0\) \(\frac{14 x^2-56 x-\left(9 x^2-30 x+9 x-30\right)}{(x+1)(x-4)} < 0\) \(\frac{\left(14 x^2-56 x-9 x^2+30 x-9 x+30\right)}{(x+1)(x-4)} < 0\)…