Help in need! : Rational functions problem

Homework Statement

A scientist predicted that the population of fish in a lake could be modeled by the function f(t)= 40t/(t^2+1), where t is given in days. The function that actually models the fish population is g(t)=45t/(t^2+8t+7). Determine where g(t)>f(t).

Homework Equations

f(t)= 40t/(t^2+1)
g(t)=45t/(t^2+8t+7)
g(t)>f(t)

The Attempt at a Solution

g(t)>f(t)
45t/(t^2+8t+7)>40t/(t^2+1)
45t/(t+1)(t+7)-40t/(t^2+1)>0
Find LCD by multiplying 1
45t/(t+1)(t+7) x (t^2+1)/(t^2+1)-40t/(t^2+1) x (t+7)(t+1)/(t+7)(t+1) > 0
Simplifies to
(5t^3-320t^2-235t)/(t+1)(t+7)(t^2+1)
5t(t^2-64t-47)/(t+1)(t+7)(t^2+1) >0

Am i doing this correct? I don't know what to do next.

$$\frac{40t}{(t^2+1)}$$ = $$\frac{45t}{(t^2+8t+7)}$$
Step one should be multiplying both sides by $$(t^2+8t+7)$$ and $$(t^2+1)$$