Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 8 - Rational Functions - 8-4 Rational Expressions - Practice and Problem-Solving Exercises - Page 531: 14

Answer

$\dfrac{7}{15x^2}$ Restriction: $x \ne 0$; $y \ne 0$

Work Step by Step

To multiply two rational expressions, we multiply the numerical coefficients first: $\dfrac{28x^2y}{60x^4y}$ Divide numerator and denominator by $4$ to simplify: $\dfrac{7x^2y}{15x^4y}$ To divide exponents having the same bases, we subtract the exponents and keep the base as-is: $\dfrac{7(x^{2 - 4})(y^{1 - 1})}{15}$ Subtract the exponents: $\dfrac{7(x^{-2})(y^{0})}{15}$ We don't want negative exponents in our answer, so we change them into positive exponents and take their reciprocal. Also, replace $y^0$ with $1$: $\dfrac{7}{15x^2}$ To see what restrictions for the variables we have, we need to see which values for the variables will make the denominator equal to $0$, which will cause the fraction to become undefined: Restriction: $x \ne 0$; $y \ne 0$
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