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Help I don't have anybody who can help me answer my question and it is home work that is due tomorrow! I got as an end answer of $x = -x$. Is that a valid answer?

If it isn't then this is the equation I started out with: $$\frac{3+x}{3-x}=\frac{3+2x}{3-2x}$$ Help me please - I take algebra and I am in middle school.

Sal
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Emily Chappell
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    Without a wordy answer, just think about what $x = -x$ means. It is the only number where the positive equals the negative. So what is it? Where the answer has been provided below. – dustin Dec 03 '14 at 02:14

2 Answers2

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Yes, $x=-x$ does follow from $\frac{3+x}{3-x}=\frac{3+2x}{3-2x}$. However, I wouldn't say $x=-x$ is an answer per se - it's just a simplification. However you can easily solve for $x$ treating $x=-x$ just as another equation. If you add $x$ to both sides you get $2x=0$ so $x=0$, which is the solution.

Milo Brandt
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$$\frac{3+x}{3-x} = \frac{3+2x}{3-2x} $$

This is equivalent to:$$(3+x)(3-2x) = (3+2x)(3-x) \Rightarrow -2x^2 -3x +9 = -2x^2 +3x + 9$$

therefore $-3x = 3x \Rightarrow x = -x $ which implies that $x = 0$

Edward Jiang
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Peter A
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