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Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{a}{4}+\frac{7 a}{8}}{\frac{6 a^{2}}{5}-\frac{3 a^{2}}{10}}+\frac{3}{a}$

$\frac{17}{4 a}, a \neq 0$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 6

Complex Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

McMaster University

Harvey Mudd College

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Okay, We're gonna simplify a complex expression. This is number 22. Our expression is a over floor plus seven A over eight, all over. Six a squared over five, minus three, a square over 10 plus three over a. Okay, let's take the numerator of the first term. We're gonna take a over the four, plus the seven a over eight, and we're gonna simplify that sort of combine. In order to do that, we're gonna have to take the first fraction by two. Both the top in the bottom seven. A eight. So our numerator, actually, now it's gonna be nine a over eight. The dumb denominator. We have six a squared over five minus three, a squared over 10. We can go ahead and multiply the first fraction by too. So we're gonna have 12. A squared over 10. Subtract three a squared over 10. That's gonna leave us with nine a squared over 10. Okay. So we can take that up here, back up on the top and replace us. So we're gonna end up with nine a over eight, all over nine. A square over 10 plus the three A. So that basically means that we have nine a over eight multiply by. The reciprocal was just 10 over nine a square and we can add the three over a so we can get rid of this nine a this nine and one that's gonna leave And we can simplify this one. We can divide both of these by two. So that's gonna leave us with five on the top and for a on the bottom and adding three a. So we're gonna take the second fraction times the floor because we need to get the denominators the same. So three times four is 12 over for a That's gonna leave us with 17 over for a and that is a CE faras. We can simplify that. And in order for that, this to not be undefined A cannot be a zero, and it cannot be. And that's it. They cannot be zero. Otherwise they would leave it. It's undefined

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