Problem of the Week

Problem 13 solution

Congratulations to Tamunotondo Banigo from Dixons McMillan Academy, Igor Podziewski and Charlie Watkins from Bottisham Village College and Keo Osman from Simon Balle School, Hertford for successfully solving this problem!

We know that $xy = 1$
Therefore, we could substitue the 1’s in the equation with $xy$ ‘s and we will get

$\frac{xy}{x^2 + xy} + \frac{xy}{y^2 + xy}$

and notice that we can factorise the denominators

$\frac{xy}{x(x + y)} + \frac{xy}{y(y + x)}$

Now, we cancel out the common factors in the numerators and denominators:

$\frac{y}{x + y} + \frac{x}{y + x}$

Then, the equations will have the same denominator which means we could combine the numerators

$\frac{x + y}{x + y}$

The numerator and denominator cancels out and this leaves us with the value of 1.