Hello there. To solve this question, we have to remember some properties about dividing polynomial expressions.
Given the following rational function:
We want to simplify it.
For this, we'll use long division. Dispose the terms in the following diagram:
We start with the first term from both expressions. Think of an expression that multiplied by y would give you y³.
It is easy to find that this is y², hence multiply and subtract from it.
Next, take the quotient's first term and do the same process. Think of an expression that multiplied by y would give you -2y².
Again, it is easy to see that this expression is -2y, hence we get.
Finally, determine an expression that multiplied by y gives you 4y. This is clearly 4, hence we get.
Notice that now the degree of the expression we're dividing is no longer greater or equal to the the divisor, therefore we stop here.
The result for this division is:
Or we can rewrite it as:
