## Solve Lesson 53 Page 17 Math 10 SBT – Kite>

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 $$C = A{\rm{\backslash }}B$$