Question #42cd3

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Answer 1 · 2016-02-10T13:49:44

If $F \neq f_{1}$ $F != f_1$

$f_{2} = \frac{F f_{1}}{f_{1} - F}$ $f_2=(Ff_1)/(f_1-F)$

If $F \neq f_{1}$ $F != f_1$ (to avoid dividing by $0$ $0$ )

$F = \frac{f_{1} f_{2}}{f_{1} + f_{2}}$ $F = (f_1f_2)/(f_1+f_2)$

$\Rightarrow F (f_{1} + f_{2}) = f_{1} f_{2}$ $=>F(f_1+f_2)=f_1f_2$

$\Rightarrow F f_{1} + F f_{2} = f_{1} f_{2}$ $=>Ff_1 + Ff_2 = f_1f_2$

$\Rightarrow F f_{2} - f_{1} f_{2} = - F f_{1}$ $=>Ff_2-f_1f_2 = -Ff_1$

$\Rightarrow f_{2} (F - f_{1}) = - F f_{1}$ $=>f_2(F-f_1)=-Ff_1$

$:.f_2=-(Ff_1)/(F-f_1)=(Ff_1)/(f_1-F)$