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\[2-\frac{x^2+10xy+7y^2}{x^2+4xy+4y^2}=\]

For starters: Multiply 2 by the denominator and put it over the existing denominator.

You'll get 2x^2 - x^2 and 8xy - 10xy, etc.

factories the numerator and denominator first, and cancel the common factor

factorize *

\[2-\frac{x^2+10xy+7y^2}{x^2+4xy+4y^2}=2-\frac{(x+.y)\cancel{(x+..y)}}{\cancel{(x+..y)}(x+...y))}=\]

My method and Unkle's are a little different. Mine is less steps.

but your solution does not yield the simplified fraction

in case your wondering...im still here im just working it out on paper....

is the final answer (x-y)^2/(x+y)^2 ?

wait (x-y)^2/(x+2y)^2

Yes!

Good job!

Thank You! Your a GREAT teacher!

You're a great student and a pleasure to work with!

:D