Write each rational expression in lowest terms. See Example 2. 3 ...

Question

Write each rational expression in lowest terms. See Example 2. 3 (3 - t)—————— (t + 5) (t - 3)

Accepted Answer

Hey, everyone here we are asked to reduce the following rational expression to the lowest terms and indicate the values that should not be included in its domain. Here, we are given the expression six multiplied by the quantity of six minus Q all divided by the quantity of Q plus seven multiplied by the quantity of Q minus six. Here we have four answer choice options, answer choices A through D, each of which vary in the reduced rational expression as well as the values that must be excluded from the domain. So looking at our given rational expression before we begin reducing this expression, we first want to identify the values of Q that cause this expression to be undefined. So since we see we have Q in the denominator of the expression, we know that our denominator cannot be equal to zero, since that will cause us to divide by zero and thus cause our expression to be undefined. So we want to take our denominator which again, we have the quantity of Q plus seven multiplied by the quantity of Q minus six. And we want to set this denominator equal to zero and solve for Q, since that will tell us the values of Q that we must exclude. So solving four Q, we need to recall the zero product property which allows us to set each individual part of the expression equal to zero and solve four Q. So starting with the first part of our expression, we have Q plus seven is equal to zero. Solving four Q, we subtract seven from both sides. And we find that Q is equal to negative seven repeating this process. With the second part of our expression, we have Q minus six is equal to zero. Solving for Q, we add six to both sides and we find Q is equal to six. So with these QV values that we found, we now know that we cannot have Q be equal to negative seven and we cannot have Q be equal to positive six. Since this will cause these values cause our expression to be undefined. And therefore, they must be excluded from our domain. So now that we have found the values that we need to exclude from our domain, we can move back to our original expression and begin reducing it to the lowest terms. So with our given expression, we can notice we have Q minus six in the denominator. However, we have six minus Q in the numerator. So we want to begin by just factoring out negative one from the numerator. So we have negative six multiplied by the quantity of Q minus six all divided by the quantity of Q plus seven multiplied by the quantity of Q minus six. And now we see that in both the numerator and the denominator, we have the expression Q minus six. So they both cancel. And we can now rewrite our expression in its reduced form where we have negative six divided by the quantity of Q plus seven. And now we see with our reduced expression that there are no further simplifications that we can make. So this is its final, simplified form. And so we are left here with answer choice C where again, the reduced expression is negative six divided by the quantity of Q plus seven where we know that Q cannot be equal to negative seven or positive six. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write each rational expression in lowest terms. See Example 2. 3 (3 - t)—————— (t + 5) (t - 3)

Key Concepts

Rational Expressions

Factoring Polynomials

Lowest Terms

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