a) $\frac{x^2+2}{x-1}=\frac{3x^3+6x}{M}$
⇔ $\frac{x-1}{x^2+2}=\frac{M}{3x^3+6x}$
⇔ $\frac{M}{3x^3+6x}=\frac{x-1}{x^2+2}$
⇔ $M=\frac{(3x^3+6x)(x-1)}{x^2+2}$
⇔ $M=\frac{3x(x^2+2)(x-1)}{x^2+2}$
⇔ $M=\frac{3x(x^2+2)(x-1)}{x^2+2}$
⇔ $M=3x(x-1)$
⇔ $M=3x^2-3x$
b) $\frac{a+ab}{a-ab}=\frac{1+b}{N}$
⇔ $\frac{a(1-b)}{a(1+b)}=\frac{N}{1+b}$
⇔ $\frac{N}{1+b}=\frac{a(1-b)}{a(1+b)}$
⇔ $\frac{N}{1+b}=\frac{a(1-b)}{a(1+b)}$
⇔ $N=\frac{(1+b)(1-b)}{1+b}$
⇔ $N=1-b$
c) $\frac{x^2+2x+1}{2x^2-2}=\frac{x+1}{I}$
⇔ $\frac{2x^2-2}{x^2+2x+1}=\frac{I}{x+1}$
⇔ $\frac{I}{x+1}=\frac{2x^2-2}{x^2+2x+1}$
⇔ $\frac{I}{x+1}=\frac{2(x^2-1)}{(x+1)^2}$
⇔ $I=\frac{2(x+1)(x+1)(x-1)}{(x+1)^2}$
⇔ $I=\frac{2(x+1)^2(x-1)}{(x+1)^2}$
⇔ $I=2(x-1)$
⇔ $I=2x-2$
