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

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Question

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

8m² + 6m - 9
 16m² - 9

Accepted Answer

Hey, everyone here we are asked to reduce the following rational expression to the lowest terms and indicate values that should not be included in its domain. Here we have four answer choice options. Each of which include some expression that varies by sign for each answer choice as well as the domains limitations that vary slightly. So here we are given the expression 11 K squared plus 70 K minus all divided by 121 K squared minus 49. So our first step in reducing our given rational expression is to factor both the numerator and the denominator. So in the numerator, we factor the trinomial into two sets of parentheses where we first have the quantity of K minus seven multiplied by the quantity of K plus seven. And now in the denominator, we have the difference of two squares. So we can factor this expression into the quantity of 11 K minus seven multiplied by the quantity of 11 K plus seven. So now we just want to start simplifying our expression by noticing we have 11 K minus seven in the numerator as well as the denominator of our fraction. So both of these expressions cancel. And now rewriting our simplified expression, we have K plus seven all divided by 11 K plus seven. So now that we have finished reducing our given rational expression, we have our final simplified answer. We now need to determine the values that are not included within the domain. So here we see that we have K in the denominator and the expression in the denominator right now is 11 K plus seven. And so we know this expression must not be equal to zero since that will result in us dividing by a zero and then cause our expression to be undefined. So we want to solve 11 K plus seven is equal to zero and solve four K. So we find the value of K that we must exclude. So solving four K, we just subtract seven from both sides. So we have 11 K is equal to negative seven. Now continuing to solve four K, we divide both sides by 11 and we find that K is equal to negative seven divided by 11. And so now we have found that K cannot be equal to negative seven divided by 11. Since that will result in our expression being undefined. So it cannot be included in our domain. However, we need to look back at our original expression where in the denominator, we have 121 K squared minus 49. And now, if we set this expression equal to zero. We can notice that our value for K can either be positive or negative seven divided by 11. Since K is squared. So again, since K is squared in the denominator of our original expression, we can have either plus or minus seven divided by 11 excluded from our domain. So with this clarified, we are left with answer choice B where again, our simplified expression is K plus seven all divided by 11 K plus seven, where K cannot be equal to negative seven divided by 11 or K cannot be equal to positive seven divided by 11. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Write each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9