First slide

Theory of equations

Question

Number of solutions of
$x - \frac{5}{x - 2} = 2 - \frac{5}{x - 2}$ is

Moderate

A

0
B

1
C

2
D

infinite.

Solution

The equation (1) is defined when $x \neq 2$
We can cancel $5 / (x - 2)$ from both the sides of (1) to obtain
$x = 2$ .
Thus, (1) has no solution.

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