Number of solution of ` x - (5)/(x - 2) = 2 -(5)/(x-2)` is

Options

A. 0
B. 1
C. 2
D. infinite

Answer

To solve the equation \( x - \frac{5}{x - 2} = 2 - \frac{5}{x - 2} \), we will follow these steps:

### Step 1: Simplify the Equation
Start by rewriting the equation:
\[ x - \frac{5}{x - 2} = 2 - \frac{5}{x - 2} \]

### Step 2: Eliminate the Fraction
Since both sides have the term \(-\frac{5}{x - 2}\), we can add \(\frac{5}{x - 2}\) to both sides:
\[ x = 2 \]

### Step 3: Check for Validity
Now, we need to check if \(x = 2\) is a valid solution. Substitute \(x = 2\) back into the original equation:
\[ 2 - \frac{5}{2 - 2} = 2 - \frac{5}{0} \]
This results in division by zero, which is undefined.

### Step 4: Conclusion
Since substituting \(x = 2\) leads to an undefined expression, \(x = 2\) is not a valid solution. Therefore, the equation has **no solutions**.

### Final Answer
The number of solutions of the equation is **0**.

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