Question 88

If x+y=4, then what is the value of $$\frac{2}{x-2}+\frac{2}{y-2}$$ ?

Solution

Given : $$x+y=4$$ ---------(i)

To find : $$\frac{2}{x-2}+\frac{2}{y-2}$$

= $$\frac{2(y-2)+2(x-2)}{(x-2)(y-2)}$$

= $$\frac{(2y-4)+(2x-4)}{(x-2)(y-2)}$$

= $$\frac{2(x+y)-8}{(x-2)(y-2)}$$

= $$\frac{2(4)-8}{(x-2)(y-2)}=\frac{0}{(x-2)(y-2)}=0$$

=> Ans - (B)

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