How to solve calc problem? lim (4-9x+sin7x)/(5x+cos7x) x->-infinity

please show steps and explain how to do this problem!!

lim x→-∞ (4 - 9x + sin(7x)) / (5x + cos(7x))

sin(7x) and cos(7x) will oscillate between -1 and 1 as x becomes a larger negative number, so you can essentially remove these terms, as they will be of no consequence.

lim x→-∞ (4 - 9x) / (5x) = -∞/∞
lim x→-∞ (4/x - 9) / 5 = -9/5