Write each rational expression in lowest terms. 3(3 - t) / (t ...

Question

Write each rational expression in lowest terms. 3(3 - t) / (t + 5)(t - 3)

Accepted Answer

Hello everyone. We're going to simplify the expression 13 times 7 -3 over V -17 times v -7. First thing I want to do is rewrite this as a fraction. So I can clearly see where my numerator and denominator are. So 13 times 7 -3. is my numerator And V - times v -7 is my denominator recalling that. I can only cancel these things if the parentheses are exactly the same. I recognize that I need to do something else before I can do any reducing here As much as I'd like 7 -3 and V -7 to be the same for this problem. They unfortunately are not so I can fix that. However, by factoring a negative one out of those parentheses it'll flip it for me, I'm gonna do it out of the bottom so I'm gonna flip the seven minus V. In the denominator by factoring a negative one out of it. So I'm gonna put the -1 out front. The V -17 isn't changing in this step. And when I factor out that negative one my seven becomes my positive, my V becomes my negative and now I have a set of matching factors So I can cancel 7 -3. I don't really want to leave that negative one sitting there. So I'm going to multiply it into my denominator so when I do that I end up with a negative V plus 17. That doesn't look really nice. So I'm going to flip it around. So the 17 comes first. So I end up with 13 over V -17. There's nothing else I can simplify. So this is my solution and that is answer choice B. Have a good day.

Write each rational expression in lowest terms. 3(3 - t) / (t + 5)(t - 3)

Key Concepts

Rational Expressions

Factoring Polynomials

Simplifying Rational Expressions

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