The rational expression \frac{x - 3}{x^2 - x - 12} is undefined for two real values of x. … — ACT

The rational expression $\frac{x - 3}{x^2 - x - 12}$ is undefined for two real values of $x$ . What are these two values, where the smaller value is entered in the first blank and the larger value is entered in the second blank?

Cevap:The smaller value is 【-3】 and the larger value is 【4】.

Cevap

The expression is undefined when the smaller value is -3 and the larger value is 4.

A rational expression is undefined when the denominator is equal to

0

. For the expression

\frac{x - 3}{x^2 - x - 12}

, setting the denominator equal to zero gives

x^2 - x - 12 = 0

. Factoring the quadratic expression yields

(x - 4)(x + 3) = 0

. Setting each factor to zero gives the solutions

x = 4

and

x = -3

. Thus, the smaller value for which the expression is undefined is

-3

and the larger value is

4

Adım Adım Çözüm

Identify the condition that makes a rational expression undefined.

A rational expression is undefined when its denominator is equal to zero.

Division by zero is undefined in real numbers.

Set the denominator of the expression equal to zero.

x^2 - x - 12 = 0

This equation will yield the values of

x

for which the denominator is zero.

Factor the quadratic equation.

(x - 4)(x + 3) = 0

Factoring allows us to find the roots by setting each linear factor to zero.

Solve for

x

by setting each factor equal to zero.

x = 4

x = -3

x - 4 = 0

, then

x = 4

. If

x + 3 = 0

, then

x = -3

Identify the smaller and larger values.

The smaller value is

-3

and the larger value is

4

Comparing the two values,

-3 < 4

Anahtar Kavram

Identifying values that make a rational expression undefined by finding the roots of the denominator.

Tahmini Süre:1m 15s

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