Question

3n/(n2 -7n + 10) - 2n/(n2-8n+15)

Answer 1

First factor the denominators.

3n/(n^2 -7n + 10) - 2n/(n^2-8n+15)
= 3n/[(n-5)(n-2)] -2n/[(n-5)(n-3)]

= [n/(n-5)] *{[3/(n-2)]-[2/(n-3)]}
= [n/(n-5)] *{[3(n-3)-2(n-2)/(n-2)(n-3)]}
= [n/(n-5)]*(n+5)/[(n-2)(n-3)]
This does not seem to be getting any simpler.