how to solve rationals equations?

Question

z^2/8-7z/8=1

n^2/2-5n/6-2=0

Answer 1

for the first equation multiply by 8 to get:

z^2 - 7z - 8 = 0

then factor to get:

(z +1)(z - 8) = 0
z = -1 OR z = 8

next problem:

multiply by 6 to get:

3n^2 - 5n - 12 = 0

Now factor the polynomial to get:

(3n + 4)(n - 3) = 0
3n = 4 n=4/3 OR
n-3=0 n=3

Answer 2

First step is to get rid of the fractions.
Multiply the first one by 8 and the second by 6.
then get everything on one side and either factor or use the quadratic formula