2/3 = 5n-81/{([n-1]/4)^2 -10} What is n?

All help greatly appreciated (Happy)

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- Mar 18th 2009, 03:17 AMolliemanAlgerbra
2/3 = 5n-81/{([n-1]/4)^2 -10} What is n?

All help greatly appreciated (Happy) - Mar 18th 2009, 04:15 AMADARSH
$\displaystyle

\frac{2}{3} = \frac{5n-81}{(\frac{(n-1)}{4})^2 -10}$

$\displaystyle

\frac{2}{3} = \frac{16(5n-81)}{(n-1)^2 -160}$

$\displaystyle

2(~(n-1)^2-160~) = 48(5n-81)$

$\displaystyle

(~(n)^2-159 -2n~) = 24(5n-81)$

Now use formula for roots of quadratic equation - Mar 18th 2009, 04:21 AMstapel
Your

**formatting**is ambiguous; I*think*you mean the following:

. . . . .$\displaystyle \frac{2}{3}\, =\, \frac{5n\, -\, 81}{\left(\frac{n\, -\, 1}{4}\right)^2\, -\, 10}$

If so, then a good first step in**solving this rational equation**is probably to multiply through, to get rid of the denominators:

. . . . .$\displaystyle 2\left[\left(\frac{n\, -\, 1}{4}\right)^2\, -\, 10\right]\, =\, 3(5n\, -\, 81)$

. . . . .$\displaystyle 2\left[\frac{n^2\, -\, 2n\, +\, 1}{16}\, -\, 10\right]\, =\, 15n\, -\, 243$

. . . . .$\displaystyle \frac{n^2\, -\, 2n\, +\, 1}{8}\, -\, 20\, =\, 15n\, -\, 243$

. . . . .$\displaystyle n^2\, -\, 2n\, +\, 1\, -\, 160\, =\, 120n\, -\, 1944$

Then collect all the terms on one side of the "equals" sign:

. . . . .$\displaystyle n^2\, -\, 122n\, +\, 1785\, =\, 0$

Then apply**the Quadratic Formula**to solve for "n". Remember to check your solutions in the*original*equation, making sure that they don't cause any "division by zero" problems. :D