Need help on how to cancel out denominators if they're different, please explain thoroughly, thanks!

Answer:
x = 2 12/13
Step-by-step explanation:
(x - 4)/7 = (8 - 3x)/5
A fraction is the same as a division problem, and you can see that x-4 is being divide by 7
The opposite of dividing by 7 is multiplying by 7
Multiply both sides by 7
x-4 = (8-3x)/5 * 7
x - 4 = 56 - 21x/5
Now multiply both sides by 5
5x - 20 = 56 - 21x
Now solve:
5x - 20 = -21x + 56
26x - 20 = 56
26x = 76
x = 2 12/13
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-Chetan K