I think you've been doing to much maths...!
I can't speak too much though.. Being up at 4:40am and helping with maths xd
cancelling out like terms in fractions is a concept you have to be familiar with from gcse
If you have a/b = b/d
The only way to solve it is by bringing the denominators to the top
You can't just simply cancel them out. I think you're getting confused with this scenario
If the numerators were both the same, then you can cancel them. (since you can "divide both sides by a")
or if the denominators were both the same, you could "times both sides by a" and they would cancel out
That didn't really answer the question tho,
Cos there the numerator on the RHS and the denominator on the LHS are the same so why does me cancelling them out give me a wrong answer