First slide

Theory of equations

Question

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

Easy

A

One
B

Two
C

Infinite
D

None of these

Solution

Wehave $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ -.If $x \neq 1$ multiplying each term by (x - 1), the glven 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 root.

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