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Chapter 7: Problem 11

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x+5}{x^{2}+x-12}$$

Short Answer

Expert verified
The given rational expression is undefined for x = 3 and x = -4.

Step by step solution

01

Identify the Denominator

Identify the denominator of the rational expression, which is \(x^2 + x - 12\) in this case.
02

Set the Denominator Equal to Zero

The denominator cannot be zero because division by zero is undefined in mathematics. So, to find the values of x that make this expression undefined, set the denominator equal to 0: \(x^2 + x - 12 = 0\)
03

Solve the Equation

Now, you need to solve this equation. First, factor the quadratic: \( (x - 3)(x + 4) = 0 \). Then, set each factor equal to 0 and solve for x: \(x - 3 = 0 => x = 3\) and \(x + 4 = 0 => x = -4 \)

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{y+1}+\frac{2}{3 y}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{6}+\frac{x+2}{3}$$

What is a proportion? Give an example with your description.

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$

Will help you prepare for the material covered in the next section. a. If \(y=k x\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)
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