Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
B7.\\
a)\,DKXD:\,x \ne \pm 2\\
C = \frac{{{x^3}}}{{{x^2} - 4}} - \frac{x}{{x - 2}} - \frac{2}{{x + 2}}\\
C = \frac{{{x^3}}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} - \frac{{x\left( {x + 2} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} - \frac{{2\left( {x - 2} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
C = \frac{{{x^3} - {x^2} - 2x - 2x + 4}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
C = \frac{{{x^3} - {x^2} - 4x + 4}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
C = \frac{{{x^2}\left( {x - 1} \right) - 4\left( {x - 1} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
C = \frac{{\left( {{x^2} - 4} \right)\left( {x - 1} \right)}}{{{x^2} - 4}}\\
C = x - 1\\
b)\,C = 0 \Leftrightarrow x - 1 = 0 \Leftrightarrow x = 1\\
c)C > 0 \Leftrightarrow x - 1 > 0 \Leftrightarrow x > 1
\end{array}\)
