# Multiplication and Division of Rational Expressions

• Feb 10th 2013, 09:36 PM
AmberRose
Multiplication and Division of Rational Expressions
28x+4 14x+7
45x-30 / 30x-20 (Wondering)
• Feb 10th 2013, 09:40 PM
AmberRose
Re: Multiplication and Division of Rational Expressions
Okay so that was meant to be: 28x+4 over 45x-30, divided by 14x+7 over 30x-20.
• Feb 10th 2013, 10:02 PM
Kromletch
Re: Multiplication and Division of Rational Expressions
$\displaystyle \frac{28x+4}{45x-30} / \frac{14x+7}{30x-20}$
• Feb 10th 2013, 10:03 PM
Kromletch
Re: Multiplication and Division of Rational Expressions
Are you trying to solve for x or what?
• Feb 10th 2013, 10:12 PM
AmberRose
Re: Multiplication and Division of Rational Expressions
simplifying
• Feb 11th 2013, 01:23 PM
Kromletch
Re: Multiplication and Division of Rational Expressions
I wish i knew how to do these off hand
• Feb 11th 2013, 02:59 PM
Deveno
Re: Multiplication and Division of Rational Expressions
the way you do these is the same way you divide by fractions:

(a/b) ÷ (c/d) = (a/b)(d/c) = (ad)/(bc)

in this case, a = 28x + 4, b = 45x - 30, c = 14x + 7, and d = 30x - 20. so we get:

$\displaystyle \frac{\frac{28x+4}{45x-30}}{\frac{14x+7}{30x-20}} = \frac{(28x+4)(30x-20)}{(45x-30)(14x+7)}$

$\displaystyle = \frac{(4(7x+1))(10(3x-2))}{(15(3x-2))(7(2x+1))} = \frac{40(7x+1)}{105(2x+1)}$

$\displaystyle = \frac{8(7x+1)}{21(2x+1)} = \frac{56x+8}{42x+21}$