Hello, Amajau,
Difficult! Here is my attempt. I interpret your word problem as:
Expanding the numerator:
The numerator cubed requires a little work, but follow the rules for such a multiplication. Multiply (5x-7) times itself once, and then take the result and multiply it by the same. Too many characters for me to type everything in, but the result is shown in the numerator above.
Then use longhand division. Painful, again. A lesson by Sal Khan helps explain: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:quad-div-by-linear/v/polynomial-division. There are several lessons in this series that might be helpful.
My attempt at doing this via long division did not work. I gave up when my first try didn't result in an equation that I could.t easily factor any further. Perhaps you or another tutor will have better luck.
Sorry,
Bob