Algebra
Algebraic Manipulation
If \(\frac{1}{a}-\frac{1}{b}=-37\), the value of \[\frac{a+8ab-b}{a-3ab-b}\] can be expressed as \(\frac{n}{m}\), where \(m\) and \(n\) are coprime positive integers. What is the value of \(m+n\)?
If the polynomial \[x^2-y^2+11x+7y+18\] can be factorized as \((x+y+a)(x-y+b),\) what is the value of \(a+b?\)
If \(-x^3+6x^2-6x+36\) is factorized as \((a-x)(x^2+b),\) what is the value of \(a+b\)?
If \(x+2y-6+3(1-x-2y)=-51\), what is \(x+2y\)?
If \(x+2y=-13\), what is the value of \[x^2+4xy-2x-4y-3+4y^2?\]