x^2/x^2-4 = x/x+2 - 2x^2-x: it get x^2=-6x-x^2
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Re: x^2/x^2-4 = x/x+2 - 2x^2-x
x^2/x^2-4 = x/x+2 - 2x^2-x means \(\displaystyle \frac{x^2}{x^2}-4 = \frac{x}{x}+2 - 2x^2-x\). Before I put any more time in on this you need to use parenthesis to clarify what you mean. If you mean x^2/(x^2-4) = x/(x+2) - 2x^2-x, then it leads to...
0 = -2x^4 - x^3 + 8x^2 + 2x. Again. Please clarify.
x^2/x^2-4 = x/x+2 - 2x^2-x means \(\displaystyle \frac{x^2}{x^2}-4 = \frac{x}{x}+2 - 2x^2-x\). Before I put any more time in on this you need to use parenthesis to clarify what you mean. If you mean x^2/(x^2-4) = x/(x+2) - 2x^2-x, then it leads to...
0 = -2x^4 - x^3 + 8x^2 + 2x. Again. Please clarify.
mmm4444bot
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ginny1029 said:
If your latest typing represents the actual equation you received, then my answer to your question above is YES! We like to receive the same equations and expressions for which posters are seeking help. It's not much help if we work on something that doesn't match what the posters are working on.
Does that make sense, to you?
Your typing above is clear; however, I see that the last "part" on the righthand side changed drastically.
2x^2 - x turned into a fraction with 2 - x in the denominator. In other words, the 2 changed from being an exponent to not being an exponent.
Is this right? You previously stated that the LCM is (x + 2)(x - 2).
This is not correct, based on your latest version.
The LCM for your latest version is (x + 2)(x - 2)(2 - x).
Since (-1)(2 - x) = x - 2, we could multiply the second ratio on the righthand side by (-1)/(-1), to get the following.
x^2/(x^2 - 4) = x/(x + 2) + 2x/(x - 2)
NOW, the least common multiple is (x + 2)(x - 2).
I'm still not confident that your lastest version is actually what you received.
Please verify the following.
The lefthand side is x^2 divided by x^2 - 4.
The first ratio on the righthand side is x divided by x + 2.
The second ratio on the righthand side is -2x divided by 2 - x.
Re: x^2/x^2-4 = x/x+2 - 2x^2-x
i think they mean the same thing but the printed version states minus 2x over x+2 on the right
SORRY!!! im new to this and im obviously not good at it yet between my frustration, ignorance and dyslexia i reversed it
i think they mean the same thing but the printed version states minus 2x over x+2 on the right
SORRY!!! im new to this and im obviously not good at it yet between my frustration, ignorance and dyslexia i reversed it
mmm4444bot
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ginny1029 said:
x^2/(x^2 - 4) = x/(x + 2) - 2x/(x + 2)
The LCM is (x + 2)(x - 2).
'
ginny1029 said:
(Note: it's easier to read with spaces around plus signs, minus signs, and equal signs.)
You did good, except for one arithmetic mistake on the very last multiplication.
(-2x)(-2) = 4x, not -4x, so we get the following.
x^2 = x^2 - 2x - 2x^2 + 4x
Can you continue? (I'm assuming that you're suppose to solve for x.)
mmm4444bot
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ginny1029 said:
That's okay. We want to get an equation with zero on one side (so that we can use the Zero-Product property, to solve for x).
Subtract x^2 from both sides. That will give you an expression equal to zero.
Factor this expression.
Set each factor equal to zero, and solve each of those equations for x.
You can check both of your results by substituting them for x in the original equation (one at a time, of course), followed by doing the arithmetic to see if you end up with a true statement (like 0=0).
mmm4444bot
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When I write, "Set each factor equal to zero", this is what I mean:
-2x = 0
x - 1 = 0
Solving these two equations gives the two solutions to the original equation.
This technique (setting factors equal to zero after we see that their product is zero) has a name: the Zero-Product Property.
You can read more about it by CLICKING HERE.
