The sum of the reciprocals of Rehman's ages,( | vedclass

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(C) Let the present age of Rehman be $x$ years.Three years ago,his age was $(x-3)$ years.Five years hence,his age will be $(x+5)$ years.It is given th

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$7$

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(C) Let the present age of Rehman be $x$ years.Three years ago,his age was $(x-3)$ years.Five years hence,his age will be $(x+5)$ years.It is given that the sum of the reciprocals of Rehman's ages $3$ years ago and $5$ years from now is $\frac{1}{3}$.$	herefore \frac{1}{x-3} + \frac{1}{x+5} = \frac{1}{3}$$\frac{x+5+x-3}{(x-3)(x+5)} = \frac{1}{3}$$\frac{2x+2}{x^2+2x-15} = \frac{1}{3}$$3(2x+2) = x^2+2x-15$$6x+6 = x^2+2x-15$$x^2-4x-21 = 0$$x^2-7x+3x-21 = 0$$x(x-7)+3(x-7) = 0$$(x-7)(x+3) = 0$$x = 7$ or $x = -3$.Since age cannot be negative,the present age of Rehman is $7$ years.

The sum of the reciprocals of Rehman's ages,(in $years$) $3$ years ago and $5$ years from now is $\frac{1}{3}$. Find his present age. (in $years$)

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