1/(2x-y) - 2/(x+2y).... The book answer is (4y-3x)/(2x^2+3xy-2y^2).. can someone show me how they got to that answer?

Question

anonymous · Answer

yes use 
$$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bc}$$ with lots of parentheses and lots of distributive law and lots of combine like terms

anonymous · Answer

hmmm I am understanding on how to use the formula  it but i am not getting the same results? Can you show me how to do it so I can check it against my work?

anonymous · Answer

sure
denominator is 
$$(2x-y)(x+2y)=x^2+3xy-2y^2$$ by multiplying out

anonymous · Answer

numerator is 
$$1(x+2y)-2(2x-y)=x+2y-4x+2y=4x-3y$$

anonymous · Answer

by distributive law plus combine like terms

anonymous · Answer

Okay I just made some distribution errors...Thanks I got it now! :)