- #1

- 173

- 2

## Homework Statement

I was asked to solve this equation:

##{(x-\frac{1}{y})}^{2} -(y-\frac{1}{x})(x-\frac{1}{y})=9x##

##x-y=1##

## Homework Equations

Simultaneous equations, factor theorem and quadratic formula

## The Attempt at a Solution

I know I could have solved for x in the second equation, and substitute it into the first equation. However, the algebra becomes incredibly messy and the resulting equation becomes hard to solve. I see there is a very specific pattern in the first equation, though I can't really figure it out.