Could someone help me with this question
Simplify the rational expression.
(3x^2y+9xy^2-12y^3)/(36x^3y-27x^2y^2-9xy^3)
To simplify the rational expression:
(3x^2y+9xy^2-12y^3)/(36x^3y-27x^2y^2-9xy^3)
we need to look for any common factors in the numerator and denominator that we can cancel out.
Step 1: Factor the terms in the numerator and denominator.
The numerator can be factored as follows:
3x^2y + 9xy^2 - 12y^3 = 3y(xy + 3y - 4y^2)
The denominator can be factored as follows:
36x^3y - 27x^2y^2 - 9xy^3 = 9xy(4x^2 - 3xy - y^2)
Step 2: Cancel out common factors.
We can cancel out the common factor 3y, leaving:
(3y(xy + 3y - 4y^2))/(9xy(4x^2 - 3xy - y^2))
Step 3: Simplify further if possible.
There are no more common factors to cancel out. So, the simplified expression is:
(xy + 3y - 4y^2)/(9x(4x^2 - 3xy - y^2))
Therefore, the simplified rational expression is:
(xy + 3y - 4y^2)/(9x(4x^2 - 3xy - y^2))
I hope this helps! Let me know if you have any further questions.