What is the simplifed form of x plus yx plus y?

Answer 1

There is no obvious simplification. A simple factorisation of the three terms is not possible.

One possibility is to add another term and then factorise but that will always leave (at least) one term outside the factorisation. For example,

x + yx + y = x + yx + y + 1 - 1

= (x + 1)(y + 1) - 1

The advantage of this form is that if you want the 0 of the original equation, it is equivalent to solving

(x + 1)(y + 1) - 1 = 0

or (x + 1)(y + 1) = 1

which gives (x + 1) = 1/(y + 1)