Chapter 7: Q. 380 (page 737)

Determine the values for which the rational expression is undefined.
$\frac{x - 3}{x^{2} - x - 30}$

Short Answer

Expert verified

Rational function is undefined when $x = 6, - 5 .$

Step by step solution

Step 1. Given Data

Given that the rational function is $R (x) = \frac{x - 3}{x^{2} - x - 30} .$

Step 2. Solving quadratic equation

On factorizing the denominator using AC method,

$x^{2} - x - 30 x^{2} - 6 x + 5 x - 30 x (x - 6) + 5 (x - 6) (x - 6) (x + 5) R (x) = \frac{(x - 3)}{(x - 6) (x + 5)}$

Step 3. Critical point

To find the critical point,

$(x - 3) = 0 x = 3 (x - 6) (x + 5) = 0 x = 6, - 5$

The denominator can be substituted using critical points when the function is undefined.

$At x = 6, R (x) = \frac{6 - 3}{0} = \infty At x = - 5, R (x) = \frac{- 5 - 3}{0} = \infty$

The rational function can be undefined at x=6,-5.

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Determine the values for which the rational expression is undefined.
$\frac{x - 3}{x^{2} - x - 30}$

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Solving quadratic equation

Step 3. Critical point

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Determine the values for which the rational expression is undefined.x-3x2-x-30

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Solving quadratic equation

Step 3. Critical point

One App. One Place for Learning.

Most popular questions from this chapter

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Determine the values for which the rational expression is undefined.
$\frac{x - 3}{x^{2} - x - 30}$