Toán Lớp 8: Rút gọn `((x-1)^2/(3x+(x-1)^2)-(1-2x^2+4x)/(x^3-1)-1/(1-x)):(2x)/(x^3+x)`

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Toán Lớp 8: Rút gọn `((x-1)^2/(3x+(x-1)^2)-(1-2x^2+4x)/(x^3-1)-1/(1-x)):(2x)/(x^3+x)`, hướng dẫn giải giúp em bài này ạ, em cảm ơn thầy cô và các bạn nhiều.

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Khánh Ly 1 tuần 2022-04-13T15:43:10+00:00 1 Answer 0 views 0

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  1. $\text{($\dfrac{(x – 1)^{2}}{3x + (x – 1)^{2}}$ – $\dfrac{1 – 2x^{2} + 4x}{x^{3} – 1}$ – $\dfrac{1}{1 – x}$) : $\dfrac{2x}{x^{3} + x}$ Đkxđ: x $\neq$ 1; x $\neq$ 0}$
    $\text{= ($\dfrac{(x – 1)^{2}}{3x + x^{2} – 2x + 1}$ – $\dfrac{1 – 2x^{2} + 4x}{x^{3} – 1}$ + $\dfrac{1}{x – 1}$) . $\dfrac{x^{3} + x}{2x}$}$
    $\text{= $\dfrac{(x – 1)^{2} . (x – 1) – (1 – 2x^{2} + 4x) + 1.(x^{2} + x + 1)}{(x – 1)(x^{2} + x + 1)}$ . $\dfrac{x(x^{2} + 1)}{2x}$}$
    $\text{= $\dfrac{x^{3} – 3x^{2} + 3x – 1 – 1 + 2x^{2} – 4x + x^{2} + x + 1}{(x – 1)(x^{2} + x + 1)}$ . $\dfrac{x^{2} + 1}{2}$}$
    $\text{= $\dfrac{x^{3} – 1}{(x – 1)(x^{2} + x + 1)}$ . $\dfrac{x^{2} + 1}{2}$}$
    $\text{= $\dfrac{(x – 1)(x^{2} + x + 1)}{(x – 1)(x^{2} + x + 1)}$ . $\dfrac{x^{2} + 1}{2}$}$
    $\text{= $\dfrac{x^{2} + 1}{2}$ }$
    $\textit{Ha1zzz}$
     

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