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November 2nd, 2014, 09:53 PM   #1
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This equation has me stumped



This is what I basically did:
25-x^2=(x+5)(x-5)

which means multiply 6 by x-5 = 6x - 30. Multiply -9 by X+5 = -9x - 45. Combine them gets me -75-3x=8x. Add 3 gets 11x/-75.

giving me a final answer of -75/11

What did i do wrong?!?!

Last edited by HelpMeNow; November 2nd, 2014 at 10:14 PM.
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November 2nd, 2014, 10:17 PM   #2
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Quote:
Originally Posted by HelpMeNow View Post


This is what I basically did:
25-x^2=(x+5)(x-5)

which means multiply 6 by x-5 = 6x - 30. Multiply -9 by X+5 = -9x - 45. Combine them gets me -75-3x=8x. Add 3 gets 11x/-75.

What did i do wrong?!?!
$$\frac{6}{x+5}-\frac{9}{x-5}=\frac{6(x-5)-9(x+5)}{x^2-25}=\frac{-3x-75}{x^2-25}$$

So:
$$\frac{-3x-75}{x^2-25}=\frac{8x}{25-x^2}=\frac{-8x}{x^2-25}$$

So if $x^2-25 \ne 0$, you have $-3x-75=-8x$

CB
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November 2nd, 2014, 10:45 PM   #3
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Quote:
Originally Posted by CaptainBlack View Post
$$\frac{6}{x+5}-\frac{9}{x-5}=\frac{6(x-5)-9(x+5)}{x^2-25}=\frac{-3x-75}{x^2-25}$$

So:
$$\frac{-3x-75}{x^2-25}=\frac{8x}{25-x^2}=\frac{-8x}{x^2-25}$$

So if $x^2-25 \ne 0$, you have $-3x-75=-8x$

CB
What?
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November 2nd, 2014, 11:13 PM   #4
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Quote:
Originally Posted by HelpMeNow View Post
What?
What "What"????
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November 3rd, 2014, 01:38 AM   #5
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Quote:
Originally Posted by HelpMeNow View Post
What?
Your explanation of what you did is incomprehensible, as far as I can tell you lost a minus sign in the wash and you did not observe that you had to assume that $x^2\ne 5$ as otherwise both sides of the equation you are trying to solve are undefined.

CB
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November 3rd, 2014, 02:35 AM   #6
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Quote:
Originally Posted by CaptainBlack
you had to assume that $\displaystyle x^2\ne 5$
(Presumably, you meant $\displaystyle x^2\ne 25$)
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November 3rd, 2014, 04:56 AM   #7
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Originally Posted by Hoempa View Post
(Presumably, you meant $\displaystyle x^2\ne 25$)
Yes, it was/is correct in the original response.

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November 3rd, 2014, 05:00 AM   #8
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Quote:
Originally Posted by HelpMeNow View Post
What?
$\displaystyle \frac{8x}{25 - x^2} = \frac{8x}{-(x^2 - 25)} = \frac{-8x}{x^2 - 25}$

This is so that the denominators on the LHS and RHS are exactly equivalent, so you can equate the numerators. Consequently, you have $\displaystyle -3x - 75 = -8x$ instead of $\displaystyle -3x-75 = 8x$.
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Last edited by Benit13; November 3rd, 2014 at 05:02 AM.
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