Question

are the complex fractions x^2-x-20/4/x-5/10 and x^2-x-20/x-5/4/10 equivalent? Simplify each, and then explain why or why not.

Answer 1

use parenthesis in your expressions, the way you wrote it is probably not what you meant

Answer 2

(x^2-x-20) /

Answer 3

ok

Answer 4

When there is a fraction divided by another fraction, you can flip the bottom fraction over and multiply instead .. like this...

Answer 5

\[\frac{ x^2 - x - 20 }{ 4 } * \frac{ 10 }{ x - 5 }\]

Answer 6

can you factor the polynomial in the numerator? ...(x ) (x )

Answer 7

factors of 20 that multiply to -20 and add up to -1

Answer 8

\[\frac{ 10 * (x -5)(x+4) }{4 * (x-5) }\]

Answer 9

--Cancel the (x-5) from both numerator and denominator (x-5)/(x-5) = 1
-- Reduce the 10/4 to 5/2

Answer 10

\[\frac{ 5(x+4) }{ 2 }\]

Answer 11

Now do the same thing to the second one..

Answer 12

A complex fraction can be simplified this way:

\(\Large \dfrac{\frac{\color{red}{a}}{\color{green}{b}}}{\frac{\color{green}{c}}{\color{red}{d}}} = \dfrac{\color{red}{ad}}{\color{green}{bc}}\)

\(\Large \dfrac{\frac{x^2 - x - 20}{4} }{\frac{x-5}{10} } = \dfrac{10(x^2 - x - 20)}{4(x - 5)}\)

\(\Large \dfrac{\frac{x^2 - x - 20}{x - 5} }{\frac{4}{10} } = \dfrac{10(x^2 - x - 20)}{4(x - 5)}\)

The complex fractions are equivalent.

Answer 13

Thank you both! :)

Answer 14

You're welcome.