<s>[INST] Rational Expression Simplification The function:
$$f(x) = \frac{3x - 4}{x^2 - 2x}$$
is simplified to:
$$f(x) = \frac{2}{x} + \frac{1}{x - 2}$$
How? And in what way?
 [/INST] $$f(x)=\frac {3x-4}{x^2-2x}\\
=\frac {3x-4}{x(x-2)}\\
=\frac Ax +\frac B{x-2}\\
=\frac {A(x-2)+Bx}{x(x-2)}$$
Equation numerators:
$$3x-4=A(x-2)+Bx\\
=(A+B)x-2A$$
gives $A=2,B=1$, i.e. 
$$f(x)=\frac {3x-4}{x^2-2x}=\frac 2x +\frac 1{x-2}$$
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