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Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{1+\frac{1}{y}-\frac{6}{y^{2}}}{1+\frac{11}{y}+\frac{24}{y^{2}}}$

$\frac{y-2}{y+8}, y \neq 0,-3,-8$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 6

Complex Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

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01:22

Simplify each complex rati…

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we're gonna simplify a complex expression. And this is number 18. And our expression is one plus one over. Why minus six over y squared. And this is all over one plus 11 over. Why? Plus 24 over y squared. First thing we need to do is simplify the numerator. So if we have one plus one over why minus six over. Why, Square, We need to get everything that has the common denominator of y squared. So we're gonna turn the one in tow. Why? Square over y squared? Plus why? Over y squared minus six over y squared. This is gonna end up equaling y squared. Plus why minus six. All over. Why, Squirt? Now we're gonna do the same thing. The denominator. We're gonna simplify that one too. So we have one plus 11 over. Why? Plus 24 over. Weiss Quirk. We need to put everything over. Why Square? So it's why squared over y squared. Plus 11. Why are 11 why? Over why plus 24 over Weiss Court. That's gonna leave us with y squared. Plus 11. Why? Plus 24 all over. Why squared? Okay. So we can go ahead and substitute this in. So we have y squared. Plus why minus six all over. Why Square we can multiply that by the reciprocal. So we're gonna change it Toe y squared over. Why squared? Plus 11. Why plus 24. We can cancel the y squared, and we're gonna end up with y squared. Plus why minus six. All over. Why squared plus 11. Why? Plus 24. Now we're gonna factor these out. Why squared? Plus, why minus six is gonna factor out to be a why, Plus three times why minus two. This is all over. Why? Plus three And why? Plus eight, we can cancel these out because there factors in both of them. That's gonna leave us with why, minus two over Why? Plus eight. And that's as far as you can go. So that's your simplest form. Now, if you look at the beginning, why cannot be zero? Because that's gonna turn those into undefined fractions. Why cannot be a naked of three, and why cannot be a negative eight

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