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Algebraic Manipulation

Advanced Simplification Tricks


If 1a1b=37\frac{1}{a}-\frac{1}{b}=-37, the value of a+8abba3abb\frac{a+8ab-b}{a-3ab-b} can be expressed as nm\frac{n}{m}, where mm and nn are coprime positive integers. What is the value of m+nm+n?

If the polynomial x2y2+11x+7y+18x^2-y^2+11x+7y+18 can be factorized as (x+y+a)(xy+b),(x+y+a)(x-y+b), what is the value of a+b?a+b?

If x3+6x26x+36-x^3+6x^2-6x+36 is factorized as (ax)(x2+b),(a-x)(x^2+b), what is the value of a+ba+b?

If x+2y6+3(1x2y)=51x+2y-6+3(1-x-2y)=-51, what is x+2yx+2y?

If x+2y=13x+2y=-13, what is the value of x2+4xy2x4y3+4y2?x^2+4xy-2x-4y-3+4y^2?


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