4x³+2x²-3x+1/(2x+1)(x-3)
what about it? The numerator has no factors in common with the denominator.
(4x^3+2x^2-3x+1)/((2x+1)(x-3)) = 2x+6 + (33x+19)/((2x+1)(x-3))
or, as partial fractions,
2x+6 + (118/7)/(x-3) + (-5/7)/(2x+1)
To simplify the given expression, we can start by factoring the denominator (2x+1)(x-3). The numerator, 4x³+2x²-3x+1, cannot be factored further.
Let's factor the denominator first:
1. The denominator has two terms: (2x+1) and (x-3).
2. To factor (2x+1), we notice that it is a binomial expression, which cannot be factored easily.
3. To factor (x-3), we recognize that it is a binomial expression, and it can be factored as (x-3).
Now we have factored the denominator as (2x+1)(x-3). To simplify the expression, we can rewrite it as:
(4x³+2x²-3x+1)/[(2x+1)(x-3)]
Since we cannot simplify further, the expression is already in its simplest form.