TS EAMCET · Maths · Functions
If \(\frac{42-13 x}{x^2+x-6}=\frac{\mathrm{A}}{l x+m}+\frac{\mathrm{B}}{p x+q}\) where \(l m>0\) and \(p q < 0\) then \(\frac{\mathrm{A} l p}{\mathrm{~B} m q}=\)
- A \(\frac{27}{32}\)
- B \(\frac{27}{8}\)
- C \(\frac{8}{243}\)
- D \(\frac{243}{32}\)
Answer & Solution
Correct Answer
(A) \(\frac{27}{32}\)
Step-by-step Solution
Detailed explanation
(a) Given, \(\frac{42-13 x}{x^2+x-6}=\frac{\mathrm{A}}{l x+m}+\frac{\mathrm{B}}{p x+q}\) Take \(\frac{42-13 x}{x^2+x-6}=\frac{42-13 x}{x^2+3 x-2 x-6}=\frac{42-13 x}{(x+3)(x-2)}\)…
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