How would I algebraically compute this limit without the use

How would I algebraically compute this limit without the use of a calculator? The solution is supposed to be :

Solution

in these type of limits divide eachh term in numerator & denominator by the highest power of x ( = 4 in this case)

SO, we will get,

= lim x-> [    (4x^-7 + 7 -x^-3)/(8x^e-4 - 9)]

= - 7/9

becasue all other terms =0 as x->