1.
(x- 1)/(x^2 +1)
=6xy^4(x-1)/6xy^4(x^2+1)
5/6xy^4
=5(x^2+1)/6xy^4(x^2+1)
2.
(x+4)/(x^2-8x+15)
=(x+4)/(x-3)(x-5)
=(x+4)^2/(x-3)(x-5)(x+4)
(x+5)/(x^2+x-12)
=(x+5)/(x-3)(x+4)
=(x+5)(x-5)/(x-3)(x+4)(x-5)
(x-3)/(x^2-x-20)
=(x-3)/(x+4)(x-5)
=(x-3)^2/(x-3)(x+4)(x-5)