làm ơn giúp mik với A=(x+1/x-1-x-1/x+1)/(2/x^2-1-x/x-1+1/x+1) giúp mk gấp ạ 09/08/2021 Bởi Alice làm ơn giúp mik với A=(x+1/x-1-x-1/x+1)/(2/x^2-1-x/x-1+1/x+1) giúp mk gấp ạ
Giải thích các bước giải: a)\(\begin{array}{l} (\frac{{x + 1}}{{x – 1}} – \frac{{x – 1}}{{x + 1}}):(\frac{2}{{x^2 – 1}} – \frac{x}{{x – 1}} + \frac{1}{{x + 1}}) \\ Đk:x \ne \pm 1 \\ = \frac{{(x + 1)^2 – (x – 1)^2 }}{{{\rm{(x – 1)(x + 1)}}}}:{\rm{[}}\frac{2}{{(x – 1)(x + 1)}} – \frac{{x(x + 1)}}{{(x – 1)(x + 1)}} + \frac{{x – 1}}{{(x + 1)(x – 1)}}{\rm{]}} \\ {\rm{ = }}\frac{{{\rm{x}}^{\rm{2}} + 2x + 1 – x^2 + 2x – 1}}{{(x – 1)(x + 1)}}:\frac{{2 – x^2 – x + x – 1}}{{(x – 1)(x + 1)}} \\ = \frac{{4x}}{{(x – 1)(x + 1)}}.\frac{{(x – 1)(x + 1)}}{{1 – x^2 }} \\ = \frac{{4x}}{{1 – x^2 }} \\ \end{array}\) Bình luận
Giải thích các bước giải:
a)\(
\begin{array}{l}
(\frac{{x + 1}}{{x – 1}} – \frac{{x – 1}}{{x + 1}}):(\frac{2}{{x^2 – 1}} – \frac{x}{{x – 1}} + \frac{1}{{x + 1}}) \\
Đk:x \ne \pm 1 \\
= \frac{{(x + 1)^2 – (x – 1)^2 }}{{{\rm{(x – 1)(x + 1)}}}}:{\rm{[}}\frac{2}{{(x – 1)(x + 1)}} – \frac{{x(x + 1)}}{{(x – 1)(x + 1)}} + \frac{{x – 1}}{{(x + 1)(x – 1)}}{\rm{]}} \\
{\rm{ = }}\frac{{{\rm{x}}^{\rm{2}} + 2x + 1 – x^2 + 2x – 1}}{{(x – 1)(x + 1)}}:\frac{{2 – x^2 – x + x – 1}}{{(x – 1)(x + 1)}} \\
= \frac{{4x}}{{(x – 1)(x + 1)}}.\frac{{(x – 1)(x + 1)}}{{1 – x^2 }} \\
= \frac{{4x}}{{1 – x^2 }} \\
\end{array}
\)