Write each rational expression in lowest terms. See Example 2....

Question

Write each rational expression in lowest terms. See Example 2. (8x² + 16x) / 4x²

Accepted Answer

Hello, everyone. For the following rational expression, we are asked to reduce it to the lowest terms and indicate values that should not be included in its domain. We are given the parentheses nine K squared plus 18 K divided by three K squared. Our answer choices are a, the parentheses, three K plus six divided by K where K cannot equal one third B the parentheses three K plus six divided by K where K cannot equal zero, C nine divided by K where K cannot equal one third D nine divided by K where K cannot equal zero. So first, I'm gonna rewrite this as a fraction. So I have nine K squared plus 18 K divided by three K squared. Before I simplify anything, I'm gonna find out what K cannot equal. So I recall that my domain cannot have undefined elements. So I want to find out what makes this fraction undefined. So it would be undefined when three K squared equals zero. So to solve for K, I divide both sides by three, so K squared equals zero, I can take the square of both sides but the squared of zero is zero. So this means that I cannot have K equal to zero. So that's gonna be part of what is, it should not be included in my domain. We cannot include when K equals zero, we have to have K cannot equal zero from there. I'm going back to my fraction. I wanna see if I can factor anything out of the numerator. So I have nine K squared plus 18 K in my numerator. I'm looking for a greatest common factor or a value I can take out of both terms and I can take nine k out of both terms. So when I do nine K squared, divided by nine K would leave us with K. So I have nine K open parentheses, K plus 18 K divided by nine K would leave me with two closed parentheses and that's all divided by three K squared. So I'm gonna reduce my constant. So I'm gonna reduce three and 93 goes into three, once, goes into 93 times from there. I can reduce the K. That is part of my GCF in the numerator with one of the KS of K squared. So the K in the numerator will cancel out K squared will become just regular K. I'm gonna rewrite what I have so far. So that way I don't lose track of it. So after reducing right now, I have three multiplied by the parentheses. K plus two, all of which is divided by K, I can't reduce anything else? But I can distribute the three back into the parentheses in the numerator. And when I do so, I would have three K plus six, all of which is divided by K. So checking my answer choices for three K plus six divided by K, I see that's both answer choice A and B. So now I need to look at what cannot be in my domain. I said K cannot equal zero. So that means this is answer choice B so we have the parentheses, three K plus six divided by K where K cannot equal zero. Have a nice day.

Write each rational expression in lowest terms. See Example 2. (8x² + 16x) / 4x²

Key Concepts

Factoring Polynomials

Simplifying Rational Expressions

Greatest Common Factor (GCF)

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