Topic
Let A be the solution set of polynomial P(x), B be the set of solutions of polynomial Q(x), C be the set of solutions of the fraction \(\frac{{P(x)}}{{Q(x) }}\). Compare the set A\B and the set C
Detailed explanation
\(A\backslash B = \left\{ {x \in \mathbb{R}\left| {P(x) = 0,Q(x) \ne 0} \right.} \right\}\)
A is the root set of the polynomial P(x), so \(A = \left\{ {x \in \mathbb{R}|P(x) = 0} \right\}\)
B is the solution set of the polynomial Q(x), so \(B = \left\{ {x \in \mathbb{R}|Q(x) = 0} \right\}\)
Consider the equation: \(\frac{{P(x)}}{{Q(x)}} = 0\left( * \right)\)
The specified condition is \(Q\left( x \right) \ne 0\), then \(
\Leftrightarrow P(x) = 0\)
Experiment set of
are x values such that \(P(x) = 0\) and \(Q(x) \ne 0\)
\( \Rightarrow C = \left\{ {x \in \mathbb{R}\left| {P(x) = 0;Q(x) \ne 0} \right.} \right\} = A{\ rm{\backslash }}B\)So \(C = A{\rm{\backslash }}B\)
Source link net do edu
