Write each rational expression in lowest terms. 8m^2 + 6m - 9 / 1...

Question

Write each rational expression in lowest terms. 8m^2 + 6m - 9 / 16m^2 - 9

Accepted Answer

Hello. We're going to reduce the expression 15 U squared minus U minus 12, divided by 25 U squared minus nine. First thing I noticed is that if this is division, I can rewrite it as a fraction and that's what I'm gonna do. My numerator is my first expression. So 15 U squared minus 11 U minus 12. My denominator is 25 U -9. In order to simplify this I need to first factor it. I can't break up subtraction sentences or addition sentences. I can only cancel things that are factors. So to factor my numerator I'm gonna make two sets of parentheses. Um To get to 15 U. Squared, I have a five U. And a three. You And then to multiply the negative Positive three and a -4. In the denominator recall that this is the difference of squares and that's a special type of factory where you take the square to the first term which is 25 U. Squared. So the square root is five you. That's our first term. In each set of parentheses Square to the last term squared to nine is 3. one is a plus one is a minus inside there's our signs now that we have it factored. We can consider canceling things. We can reduce. We can only reduce if the entire set of parentheses matches in this case five you plus three and five you plus three. Match. There's one of those in each. The numerator and the denominator. So once we cancel that out, we're left with three U -4 Over five U -3. Now at this point we can't cancel anything else. We cannot cancel out the use, we cannot cancel out the threes because we can't break up that addition and subtraction. So this is our solution three U -4/5 U -3, which is answer choice a. Have a good day.

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Write each rational expression in lowest terms. 8m^2 + 6m - 9 / 16m^2 - 9