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Chapter 9: Q50. (page 478)

For what values of $x$ is the expression $\frac{4 x}{x^{2} - x}$ undefined.
localid="1648471683435" $(A) - 1, 1 (B) - 1, 0, 1 (C) 0, 1 (D) 0 (E) 1, 2$

Short Answer

Expert verified

The expression is undefined for $x = 0, 1$ . So, option (C) is correct.

Step by step solution

01

Step 1. Write down the given information.

The given expression is $\frac{4 x}{x^{2} - x}$ .

02

Step 2. Concept used.

The expression will be undefined for which the denominator of the given expression will be equal to zero.

03

Step 3. Calculation.

The given expression $\frac{4 x}{x^{2} - x}$ has denominator $x^{2} - x$ . Therefore, equating $x^{2} - x = 0$ gives,

$\begin{array}{l} x^{2} 鈭� x = 0 \\ x (x 鈭� 1) = 0 \\ x = 0 鈥刼谤 x 鈭� 1 = 0 \\ x = 0 鈥刼谤 x = 1 \\ x = \{0, 1\} \\ x = 0, 1 \end{array}$

Since the expression is undefined for $x = 0, 1$ . So, option (C) is correct.

04

Step 4. Conclusion.

The expression is undefined for $x = 0, 1$ . So, option (C) is correct.

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