Question

Using the identity $(x+a)(x+b)=x^2+(a+b)x+ab$, find out the following products:
$(a+\frac{1}{x})(a+\frac{1}{y})$

Answer 1

We need to find product of $(a+\frac{1}{x})(a+\frac{1}{y})$ by using identity $(x+a)(x+b)=x^2+(a+b)x+ab$

Using above stated property, we have

$(a+\frac{1}{x})(a+\frac{1}{y})=a^2+(\frac{1}{x}+\frac{1}{y})a+\frac{1}{xy}$

$=a^2+a\left(\frac{x+y}{xy}\right)+\frac{1}{xy}$