Giải thích các bước giải:
\(
A = \frac{{x - 5}}{{x - 4}}(x \ne 0;x \ne 4;x \ne 5)
\)
\(
\begin{array}{l}
2x^2 - 3x = 0 \\
\Leftrightarrow x(2x - 3) = 0 \\
\Leftrightarrow \left[ {\begin{array}{*{20}c}
{x = 0} \\
{x = \frac{3}{2}} \\
\end{array}} \right. \\
\end{array}
\)
+) Thay x=0 vào A ta có:
\(
A = \frac{{0 - 5}}{{0 - 4}} = \frac{5}{4}
\)
+) Thay x=$\frac{3}{2}$ vào A ta có:
\(
A = \frac{{\frac{3}{2} - 5}}{{\frac{3}{2} - 4}} = \frac{7}{5}
\)
\(
\begin{array}{l}
b)B = \frac{{x + 5}}{{2x}} - \frac{{x - 6}}{{5 - x}} - \frac{{2x^2 - 2x - 50}}{{2x^2 - 10x}} \\
(x \ne 0;x \ne 4;x \ne 5) \\
= \frac{{x + 5}}{{2x}} + \frac{{x - 6}}{{x - 5}} - \frac{{2x^2 - 2x - 50}}{{2x(x - 5)}} \\
= \frac{{(x + 5)(x - 5)}}{{2x(x - 5)}} + \frac{{(x - 6).2x}}{{2x(x - 5)}} - \frac{{2x^2 - 2x - 50}}{{2x(x - 5)}} \\
= \frac{{x^2 - 25 + 2x^2 - 12x - 2x^2 + 2x + 50}}{{2x(x - 5)}} \\
= \frac{{x^2 - 10x + 25}}{{2x(x - 5)}} \\
= \frac{{(x - 5)^2 }}{{2x(x - 5)}} \\
= \frac{{x - 5}}{{2x}} \\
c)P = A:B = \frac{{x - 5}}{{x - 4}}:\frac{{x - 5}}{{2x}} \\
= \frac{{x - 5}}{{x - 4}}.\frac{{2x}}{{x - 5}} = \frac{{2x}}{{x - 4}} \\
= \frac{{2x - 8 + 8}}{{x - 4}} = 2 + \frac{8}{{x - 4}} \\
P \in Z \Leftrightarrow \frac{8}{{x - 4}} \in Z \Leftrightarrow x - 4 \in U(8) = {\rm{\{ }} \pm {\rm{1;}} \pm {\rm{2;}} \pm {\rm{4;}} \pm {\rm{8\} }} \\
{\rm{ = > x}} \in {\rm{\{ - 4;0;2;3;5;6;8;12\} }} \\
{\rm{Mà :x}} \ne {\rm{0;x}} \ne {\rm{4;x}} \ne {\rm{5}} \\
{\rm{ = > x}} \in {\rm{\{ - 4;2;3;6;8;12\} }} \\
\end{array}
\)
