Solving Equations Involving Rational Expressions

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Jun 19, 2017
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Can someone check this equation for me to see if I got it right? The text book has the wrong solution.

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I got a big long complex equation that was worse than the original problem!
How so? You plugged "-12/5" in for every instance of "x" on the left-hand side:

. . . . .\(\displaystyle \dfrac{3\left(-\frac{12}{5}\right)}{\left(-\frac{12}{5}\right)^2\, -\, 4}\, -\, \dfrac{2}{\left(-\frac{12}{5}\right)\, +\, 2}\)

You simplified the complex fraction in the usual manner:

. . . . .\(\displaystyle \dfrac{-\frac{36}{5}}{\frac{144}{25}\, -\, \frac{100}{25}}\, -\, \dfrac{2}{-\frac{12}{5}\, +\, \frac{10}{5}}\)

. . . . .\(\displaystyle \dfrac{-\frac{36}{5}}{\frac{44}{25}}\, -\, \dfrac{2}{-\frac{2}{5}}\)

. . . . .\(\displaystyle \left(-\dfrac{36}{5}\right)\left(\dfrac{25}{44}\right)\, -\, \left(\dfrac{2}{1}\right)\left(-\dfrac{5}{2}\right)\)

. . . . .\(\displaystyle \left(-\dfrac{9}{1}\right)\left(\dfrac{5}{11}\right)\, -\, (-5)\)

. . . . .\(\displaystyle \left(-\dfrac{45}{11}\right)\, +\, \dfrac{55}{11}\)

...and so forth. And you evaluated the right-hand side in the same way. What did you get?

Please reply showing your work. Thank you! ;)
 
How so? You plugged "-12/5" in for every instance of "x" on the left-hand side:

. . . . .\(\displaystyle \dfrac{3\left(-\frac{12}{5}\right)}{\left(-\frac{12}{5}\right)^2\, -\, 4}\, -\, \dfrac{2}{\left(-\frac{12}{5}\right)\, +\, 2}\)

You simplified the complex fraction in the usual manner:

. . . . .\(\displaystyle \dfrac{-\frac{36}{5}}{\frac{144}{25}\, -\, \frac{100}{25}}\, -\, \dfrac{2}{-\frac{12}{5}\, +\, \frac{10}{5}}\)

. . . . .\(\displaystyle \dfrac{-\frac{36}{5}}{\frac{44}{25}}\, -\, \dfrac{2}{-\frac{2}{5}}\)

. . . . .\(\displaystyle \left(-\dfrac{36}{5}\right)\left(\dfrac{25}{44}\right)\, -\, \left(\dfrac{2}{1}\right)\left(-\dfrac{5}{2}\right)\)

. . . . .\(\displaystyle \left(-\dfrac{9}{1}\right)\left(\dfrac{5}{11}\right)\, -\, (-5)\)

. . . . .\(\displaystyle \left(-\dfrac{45}{11}\right)\, +\, \dfrac{55}{11}\)

...and so forth. And you evaluated the right-hand side in the same way. What did you get?

Please reply showing your work. Thank you! ;)


Ok lol it matches up in the end when I take the time to calc it right. I guess I got impatient. Thanks for setting me back on track.

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