How do you solve #x^2/(x^2-4) = x/(x+2)-2/(2-x)#?
I found no solutions (the left side is NOT equal to the right one)
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To solve the equation x^2/(x^2-4) = x/(x+2) - 2/(2-x), we can follow these steps:
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Start by finding a common denominator for the fractions on the right side of the equation. The common denominator is (x+2)(2-x).
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Rewrite the fractions on the right side with the common denominator: x/(x+2) = x(2-x)/[(x+2)(2-x)] -2/(2-x) = -2(x+2)/[(x+2)(2-x)]
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Simplify the fractions on the right side: x/(x+2) = (2x-x^2)/[(x+2)(2-x)] -2/(2-x) = -2(x+2)/[(x+2)(2-x)]
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Combine the fractions on the right side: (2x-x^2)/[(x+2)(2-x)] - 2(x+2)/[(x+2)(2-x)]
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Now, we can eliminate the denominators by multiplying both sides of the equation by [(x+2)(2-x)]: x^2 - 2x - x^2 - 4x - 4 = 2x - x^2 - 4x - 8
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Simplify the equation: -6x - 4 = -2x - 8
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Combine like terms: -6x + 2x = -8 + 4 -4x = -4
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Divide both sides by -4: x = 1
Therefore, the solution to the equation x^2/(x^2-4) = x/(x+2) - 2/(2-x) is x = 1.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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