Question

Giúp em phần d với ạ

Answer 1

a) Để C cõ nghĩa <=> \(\left\{{}\begin{matrix}2x-2\ne0< =>x\ne1\\2-2x^2\ne0< =>x\ne\pm1\end{matrix}\right.\)

b) C = \(\dfrac{x}{2\left(x-1\right)}-\dfrac{x^2+1}{2x^2-2}=\dfrac{x}{2\left(x-1\right)}-\dfrac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)

= \(\dfrac{x\left(x+1\right)-x^2-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{x^2+x-x^2-1}{2\left(x+1\right)\left(x-1\right)}=\dfrac{1}{2\left(x+1\right)}\)

c) Để C = \(\dfrac{-1}{2}\)

<=> \(\dfrac{1}{2\left(x+1\right)}=\dfrac{-1}{2}\)

<=> x+ 1 = -1

<=> x = -2 (tm)

d) Để C nguyên

<=> \(\dfrac{1}{2\left(x+1\right)}\) nguyên

<=> 2(x+1) có dạng \(\dfrac{1}{k}\left(k\in Z,k\ne0\right)\)

<=> \(x+1=\dfrac{1}{2k}< =>x=\dfrac{1}{2k}-1\)