Câu hỏi: Thực hiện phép tính: a) 3x(5x² – 2x – 1) b) (x² – 2x + 1) : (x – 1) với x khác 1 c) x²-x/x-1 + x-1/1-x với x khác 1 d) x² – 10x + 25/x²-5x :

Đáp án:

$\begin{array}{l}
a)3x\left( {5{x^2} – 2x – 1} \right)\\
 = 15{x^3} – 6{x^2} – 3x\\
b)\\
\frac{{{x^2} – 2x + 1}}{{x – 1}} = \frac{{{{\left( {x – 1} \right)}^2}}}{{x – 1}} = x – 1\\
c)\frac{{{x^2} – x}}{{x – 1}} + \frac{{x – 1}}{{1 – x}}\\
 = \frac{{x\left( {x – 1} \right)}}{{x – 1}} – \frac{{x – 1}}{{x – 1}}\\
 = x – 1\\
d)\frac{{{x^2} – 10x + 25}}{{{x^2} – 5x}}:\frac{x}{{x – 5}}\\
 = \frac{{{{\left( {x – 5} \right)}^2}}}{{x\left( {x – 5} \right)}}.\frac{{x – 5}}{x}\\
 = \frac{{{{\left( {x – 5} \right)}^2}}}{{{x^2}}}
\end{array}$