Chapter 9: Q43. (page 477)

Under what conditions is the expression $\frac{a^{2} + a b + b^{2}}{a^{2} - b^{2}}$ undefined.

Short Answer

Expert verified

The expression is undefined for $a = - b, b$ .

Step by step solution

Step 1. Write down the given information.

The given expression is $\frac{a^{2} + a b + b^{2}}{a^{2} - b^{2}}$

Step 2. Concept used.

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

Step 3. Calculation.

The given expression $\frac{a^{2} + a b + b^{2}}{a^{2} - b^{2}}$ has denominator $a^{2} - b^{2}$ . Therefore,

equating $a^{2} - b^{2} = 0$ gives,

role="math" localid="1648315877907" $\begin{matrix} a^{2} - b^{2} = 0 \\ (a - b) (a + b) = 0 \\ a - b = 0 or a + b = 0 \\ a = b or a = - b \\ a = \{- b, b\} \\ a = - b, b \end{matrix}$

Since the expression is undefined for $a = - b, b$ .

Step 4. Conclusion.

The expression is undefined for $a = - b, b$ .

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Under what conditions is the expression $\frac{a^{2} + a b + b^{2}}{a^{2} - b^{2}}$ undefined.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Under what conditions is the expressiona2+ab+b2a2−b2undefined.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Discrete Mathematics

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Under what conditions is the expression $\frac{a^{2} + a b + b^{2}}{a^{2} - b^{2}}$ undefined.