A) 3 roots
B) 2 roots
C) 1 root
D) no root
Correct Answer: C
Solution :
The given equation is \[\frac{(x+2)(x-5)}{(x+3)(x+6)}=\frac{(x-2)}{(x+4)}\] \[\Rightarrow \]\[(x+4)(x+2)(x-5)-(x-2)(x-3)(x+6)=0\] \[\Rightarrow \]\[({{x}^{3}}+{{x}^{2}}-22x-40)-({{x}^{3}}+{{x}^{2}}-24x+36)=0\] \[\Rightarrow \]\[2x-76=0\]\[i.e.\] \[(x-38)=0\], has only one root.
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