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Chapter 7: Q. 380 (page 737)

Determine the values for which the rational expression is undefined.

x-3x2-x-30

Short Answer

Expert verified

Rational function is undefined whenx=6,-5.

Step by step solution

01

Step 1. Given Data

Given that the rational function isR(x)=x-3x2-x-30.

02

Step 2. Solving quadratic equation

On factorizing the denominator using AC method,

x2-x-30x2-6x+5x-30x(x-6)+5(x-6)(x-6)(x+5)R(x)=(x-3)(x-6)(x+5)

03

Step 3. Critical point

To find the critical point,

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

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

Atx=6,R(x)=6-30=鈭�Atx=-5,R(x)=-5-30=鈭�

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

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Most popular questions from this chapter

In the following exercise, find

(a) Rx=fx+gx

(b) R(x)=f(x)-g(x):

f(x)=-5x-5x2+x-6gx=x+12-x

In the following exercises, Divide the rational expression

2y2-10yz-48z22y-1梅4y2-32yz

Create a rational inequality whose solution is(-鈭�,-2]鈭�[4,鈭�).

In the following exercise, perform the indicated operation:

32x2+5x+2-12x2+3x+1

Simplify the complex rational expression by writing it as division:

1x+1y1x-1y
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