

InterviewSolution
Saved Bookmarks
1. |
If P = \(\frac{1+2x}{1-2x}\) and Q = \(\frac{1-2x}{1+2x}\) then \(\frac{P-Q}{P+Q}\) = ..................A) \(-\frac{4x}{1+4x^2}\)B) \(\frac{1+4x^2}{4x}\)C) \(\frac{-(1+4x^2)}{4x}\)D) \(\frac{4x}{1+4x^2}\) |
Answer» Correct option is (D) \(\frac{4x}{1+4x^2}\) We have P = \(\frac{1+2x}{1-2x}\) and Q = \(\frac{1-2x}{1+2x}\) \(\therefore\) \(\frac{P-Q}{P+Q}\) \(=\cfrac{\frac{1+2x}{1-2x}-\frac{1-2x}{1+2x}}{\frac{1+2x}{1-2x}+\frac{1-2x}{1+2x}}\) \(=\cfrac{\frac{(1+2x)^2-(1-2x)^2}{(1-2x)(1+2x)}}{\frac{(1+2x)^2+(1-2x)^2}{(1-2x)(1+2x)}}\) \(=\frac{(1+2x)^2-(1-2x)^2}{(1+2x)^2+(1-2x)^2}\) \(=\frac{(1+4x+4x^2)-(1-4x+4x^2)}{(1+4x+4x^2)+(1-4x+4x^2)}\) \(=\frac{8x}{2(1+4x^2)}\) \(=\frac{4x}{1+4x^2}\) Correct option is A) \(-\frac{4x}{1+4x^2}\) |
|