I'm not sure how to divide rational expressions:

Question

((1/x+1)+(1/x+2))/((1/x+2)+(1/(x+3))

-I got ((2x+3)(x^2+5x+6)/(2x+5)(x^2+3x+2)
but it was wrong? Please help!

Answer 1

Who said it was wrong ?

You are right up to this point, but your answer can be reduced.
((2x+3)(x^2+5x+6)/(2x+5)(x^2+3x+2)
= [(2x+3)(x+2)(x+3)/[(2x+5)(x+2)(x+1)]
= [(2x+3)(x+3)/[(2x+5)(x+1)] after canceling the x+2

you should also include the restriction that x not equal to -2