14)
(3x^2y)/(4x^3y^5) / (6y^2)/(2xy^3)
Okay first you need to realize that (a^b)/(a^c)=a^(b-c)
And you also need to know that (a^b)*(a^c)=a^(b+c), with that out of the way..
3/(4xy^4) / 3/(xy)
Now you need to know that (a/b) / (c/d) = (a/b)*(d/c) = (ad)/(bc) now we have:
3/(4xy^4) * xy/3 the 3's cancel out leaving
(xy)/(4xy^3)
1/(4y^2)
...
15)
(x^2-3x-4)/(x^2-3x-18) * (x-6)/(x+1) factor the numerator and denominator
[(x-4)(x+1)]/[(x-6)(x+3)] * (x-6)/(x+1) note that the (x+1)s and (x-6)s cancel
(x-4)/(x+3)
...
16)
(x^2-8x+15)/(x^2+12x+32) * (x+4)/(x^2-25) do the factoring...
[(x-3)(x-5)]/[(x+4)(x+8)] * (x+4)/[(x-5)(x+5)] the (x-5)s and (x+4)s cancel
(x-3)/(x+8) * 1/(x+5)
(x-3)/[(x+8)(x+5)]
...
19) maybe for some variety...
4/(x+5) + 2x/(x^2-25) factor
4/(x+5) + 2x/[(x+5)(x-5)] so to have a common denominator we multiply left term by (x-5)...
[4(x-5)+2x]/(x^2-25)
(4x-20+2x)/(x^2-25)
(8x+20)/(x^2-25)
