First slide

Theory of equations

Question

How many roots the equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ have

Moderate

A

One
B

Two
C

Infinite
D

None

Solution

If $x \neq 1,$ multiplying each term by $(x - 1)$ , the given equation reduces to $x (x - 1) = (x - 1) or {(x - 1)}^{2} = 0$ or $x = 1$ , which is not possible as considering $x \neq 1 .$
Thus given equation has no roots.

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