Question 120

If $$x+\frac{2}{x}=1$$ then the value of $$\frac{x^2+x+2}{x^2(1-x)}$$ is

Solution

Expression : $$x+\frac{2}{x}=1$$

=> $$x^2 + 2 = x$$

To find : $$\frac{x^2+x+2}{x^2(1-x)}$$

= $$\frac{x + x}{x^2(1-x)}$$

= $$\frac{2}{x - x^2}$$

= $$\frac{2}{2} = 1$$


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