Asked by Alex

Could someone help me with this question


Simplify the rational expression.

(3x^2y+9xy^2-12y^3)/(36x^3y-27x^2y^2-9xy^3)



Answered by Henry
Factor the numerator and denominator:

3y(x^2 + 3xy - 4y^2)/9xy(4x^2-3xy-y^2),

Factor the numerator and denominator into 2 binomials:

3y(x - y)(x + 4y) / 9xy(x - y)(4x + y),

Divide the numerator and denominator by 3y:

(x - y)(x + 4y) / 3x(x - y)(4x + y),

Cancel the 2 (x - y) factors:

(x + 4y) / 3x(4x + y).
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