1. ## Indices

1. if $\displaystyle 2160 = 2^a*3^b*5^c$, find values of a, b and c
2. Show that $\displaystyle \frac{y^-1}{x^-1+y^-1} + \frac{y^-1}{x^-1-y^-1} = \frac{2xy}{y^2-x^2}$

my attempt on the second one:
LHS $\displaystyle \frac{x+y}{y}+\frac{x-y}{y}$ ===> $\displaystyle \frac{x+y+x-y}{y} = \frac {2x}{y}$
Should the RHS in question be $\displaystyle \frac{2x}{y}$ ? :S

2. ## Re :

Originally Posted by Anish
2. Show that $\displaystyle \frac{y^-1}{x^-1+y^-1} + \frac{y^-1}{x^-1-y^-1} = \frac{2xy}{y^2-x^2}$

my attempt on the second one:
LHS $\displaystyle \frac{x+y}{y}+\frac{x-y}{y}$ ===> $\displaystyle \frac{x+y+x-y}{y} = \frac {2x}{y}$
Should the RHS in question be $\displaystyle \frac{2x}{y}$ ? :S
$\displaystyle \frac{1/y}{1/x+1/y}+\frac{1/y}{1/x-1/y}$

$\displaystyle =\frac{xy}{y^2+yx}+\frac{xy}{y^2-yx}$

$\displaystyle =\frac{xy^3-x^2y^2+xy^3+x^2y^2}{y^4-x^2y^2}$

Take out the common factor $\displaystyle y^2$ , you should get the RHS .

* Note that the equation above is valid ..

3. oops , how silly of me !