Question

For real x, the value of expression $\frac{x^2-2x+2}{2x-2}$ cannot !is in the interval

• A. (infinity, -1)
• B. (-1, 1)
• C. (1, 2)
• D. (2, infinity)

Answer 1

The correct option is B (-1, 1)

Let $\frac{x^2-2x+2}{2x-2}=y\Rightarrow x^2-2x+2=2xy-2y\Rightarrow x^2-2x(x+y)+2+2y=0$

The value of expression does not lie in the region when $D<0$ for $D<0$

$b^2-4ac<0\Rightarrow 4(1+y{)}^2=4\times 2(1+y)<0\Rightarrow (1+y{)}^2-2(1+y)<0\Rightarrow (1+y)[1+y-2]<0\Rightarrow (1+y)(y-1)=0$

Hence for $yϵ(-1,1)$ there is no vaue or expression.