thuc hien phep tinh 2x^2-x/x-1 +x+1/1-x +2-x^2/x-1 31/07/2021 Bởi Eden thuc hien phep tinh 2x^2-x/x-1 +x+1/1-x +2-x^2/x-1
Giải thích các bước giải: Ta có: \(\begin{array}{l}\frac{{2{x^2} – x}}{{x – 1}} + \frac{{x + 1}}{{1 – x}} + \frac{{2 – x}}{{x – 1}}\\ = \frac{{2{x^2} – x}}{{x – 1}} – \frac{{x + 1}}{{x – 1}} + \frac{{2 – x}}{{x – 1}}\\ = \frac{{2{x^2} – x – \left( {x + 1} \right) + 2 – x}}{{x – 1}}\\ = \frac{{2{x^2} – 3x + 1}}{{x – 1}}\\ = \frac{{\left( {2{x^2} – 2x} \right) – \left( {x – 1} \right)}}{{x – 1}}\\ = \frac{{2x\left( {x – 1} \right) – \left( {x – 1} \right)}}{{x – 1}}\\ = \frac{{\left( {2x – 1} \right)\left( {x – 1} \right)}}{{\left( {x – 1} \right)}}\\ = 2x – 1\end{array}\) Bình luận
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{{2{x^2} – x}}{{x – 1}} + \frac{{x + 1}}{{1 – x}} + \frac{{2 – x}}{{x – 1}}\\
= \frac{{2{x^2} – x}}{{x – 1}} – \frac{{x + 1}}{{x – 1}} + \frac{{2 – x}}{{x – 1}}\\
= \frac{{2{x^2} – x – \left( {x + 1} \right) + 2 – x}}{{x – 1}}\\
= \frac{{2{x^2} – 3x + 1}}{{x – 1}}\\
= \frac{{\left( {2{x^2} – 2x} \right) – \left( {x – 1} \right)}}{{x – 1}}\\
= \frac{{2x\left( {x – 1} \right) – \left( {x – 1} \right)}}{{x – 1}}\\
= \frac{{\left( {2x – 1} \right)\left( {x – 1} \right)}}{{\left( {x – 1} \right)}}\\
= 2x – 1
\end{array}\)