Chapter 7: Q. 378 (page 736)

Determine the values for which the rational expression is undefined.
$\frac{b - 7}{b^{2} - 25} .$

Short Answer

Expert verified

Rational function can be undefined at $b = 5, - 5 .$

Step by step solution

Step 1. Given data

Given that the rational function is $R (x) = \frac{b - 7}{b^{2} - 25} .$

Step 2. Rational function

Take $R (x) = \frac{b - 7}{b^{2} - 25}$

On applying the property of difference of two squares,

$x^{2} - y^{2} = (x - y) (x + y) b^{2} - 25 b^{2} - 5^{2} (b - 5) (b + 5) R (x) = \frac{(b - 7)}{(b - 5) (b + 5)}$

When the denominator is zero, the rational function can be undefined.

$(b - 5) (b + 5) = 0 b = 5, - 5 At b = 5, R (x) = \frac{5 - 7}{25 - 25} = \infty At b = - 5, R (x) = \frac{- 5 - 7}{25 - 25} = \infty$

when $b = 5, - 5$ rational function is undefined.

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Determine the values for which the rational expression is undefined.
$\frac{b - 7}{b^{2} - 25} .$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Rational function

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Determine the values for which the rational expression is undefined.b-7b2-25.

Short Answer

Step by step solution

Step 1. Given data

Step 2. Rational function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Mechanics Maths

Applied Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Determine the values for which the rational expression is undefined.
$\frac{b - 7}{b^{2} - 25} .$