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In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.$$\left(x^{2}-2 x+1\right) \div \frac{x-1}{3} \cdot \frac{x+4}{3 x}$$

$\frac{(x-1)(x+4)}{x} ; x \neq 0,1$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 3

Multiplying and Dividing Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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In $25-30,$ perform the in…

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In $3-20$ , perform the in…

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So for this question, were given a polling a mule divided by a fraction times fraction. So I'm just gonna look at the pollen well divided by a fraction. First of so, the polynomial were given its X squared minus two X close one, and this is being divided by X minus one over three. Dividing by fraction is the same as multiplying by. It's reciprocal. You can say that. X squared minus two X close. One is being multiplied by three over X minus one. So the numerator over here will factor out into X minus one times X minus one over one times three X minus one. So over here, it's important to note that our ex cannot equal positive one, as that would make our denominator here equal to zero. So these X minus ones cancel out and we're just left with three times X minus one over one. And now we have to multiply this by X plus four over three X. So now we have to say that our ex can also not be equal to zero, as that would make this denominator equal to zero. So the three here cancels out with this three and now we're just left with X minus one times X plus four over X and so that is our final.

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$$9-9(x+2)^{2}$$

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