Trying to help someone simplify this: (2ab - 3b^2)/(3b - 4a)

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The expression (2ab - 3b^2)/(3b - 4a) was simplified to 2ab/(4a - 3b) - b, but this simplification is questioned. Attempts to factor the numerator by adding and subtracting terms did not yield further simplification. It was noted that there are no common factors between the numerator and denominator, indicating that the expression cannot be simplified further. The discussion reflects uncertainty about whether any simplification is possible. Ultimately, the consensus is that the expression remains in its original form without further reduction.
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I managed to get it down to 2ab/(4a-3b)-b, but that doesn't seem very simplified to me. I also added and subtracted terms in the numerator to make it factorable, ect but nothings really worked out.
 
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e^(i Pi)+1=0 said:
I managed to get it down to 2ab/(4a-3b)-b, but that doesn't seem very simplified to me. I also added and subtracted terms in the numerator to make it factorable, ect but nothings really worked out.
There are no factors that are common to both the numerator and denominator, so I don't see that ##\frac{2ab - 3b^2}{3b^2 - 4a}## can be simplified at all.
 
Thanks. I wasn't sure if I was missing something.
 

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