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

Question

thanks

Answer 1

n^2-7n+10 = (n-2)(n-5)
n^2-8n+15 = (n-3)(n-5)
LCD = (n-2)(n-3)(n-5), so we have

[3n(n-3) - 2n(n-2)] / ((n-2)(n-3)(n-5))
= (3n^2-9n-2n^2+4n) / (...)
= (n^2-5n) / (...)
= n(n-5) / (n-2)(n-3)(n-5)
= n / (n-2)(n-3)
= 3/(n-3) - 2/(n-2)