Chapter 7: Q. 1 (page 651)

In the following exercises, determine the values for which the rational expression is defined.
$(a) \frac{2 x^{2}}{z} (b) \frac{4 p - 1}{6 p - 5} (c) \frac{n - 3}{n^{2} + 2 n - 8}$

Short Answer

Expert verified

$(a) \frac{2 x^{2}}{z} isundefinedat z = 0 (b) \frac{4 p - 1}{6 p - 5} isundefinedat p = \frac{5}{6} (c) \frac{n - 3}{n^{2} + 2 n - 8} isundefinedat n = - 4, 2$

Step by step solution

Step 1. Given information

$(a) \frac{2 x^{2}}{z} (b) \frac{4 p - 1}{6 p - 5} (c) \frac{n - 3}{n^{2} + 2 n - 8}$

Part a.step 1.find the undefined values

$(a) \frac{2 x^{2}}{z}$

Equate the denominator to zero and solve for the unknown variable.

$z = 0$

Hence, the undefined value at $z = 0 .$

Part b.step 1.find the undefined values

$(b) \frac{4 p - 1}{6 p - 5}$

Equate the denominator to zero and solve for the unknown variable.

$6 p - 5 = 0 6 p = 5 p = \frac{5}{6}$

Hence, the undefined value at $p = \frac{5}{6} .$

Part c.step 1.find the undefined values

$(c) \frac{n - 3}{n^{2} + 2 n - 8}$

Equate the denominator to zero and solve for the unknown variable.

$n^{2} + 2 n - 8 = 0 (n + 4) (n - 2) = 0 n + 4 = 0 \Rightarrow n = - 4 n - 2 = 0 \Rightarrow n = 2$

Hence, the undefined values are at $n = - 4, 2 .$

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In the following exercises, determine the values for which the rational expression is defined.
$(a) \frac{2 x^{2}}{z} (b) \frac{4 p - 1}{6 p - 5} (c) \frac{n - 3}{n^{2} + 2 n - 8}$

Short Answer

Step by step solution

Step 1. Given information

Part a.step 1.find the undefined values

Part b.step 1.find the undefined values

Part c.step 1.find the undefined values

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In the following exercises, determine the values for which the rational expression is defined.a2x2zb4p-16p-5cn-3n2+2n-8

Short Answer

Step by step solution

Step 1. Given information

Part a.step 1.find the undefined values

Part b.step 1.find the undefined values

Part c.step 1.find the undefined values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In the following exercises, determine the values for which the rational expression is defined.
$(a) \frac{2 x^{2}}{z} (b) \frac{4 p - 1}{6 p - 5} (c) \frac{n - 3}{n^{2} + 2 n - 8}$