How do you multiply #(2x) / (x+2) - 2 = (x-8) / (x-2)#?
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To solve the equation (2x) / (x+2) - 2 = (x-8) / (x-2), we can follow these steps:
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Start by multiplying both sides of the equation by (x+2)(x-2) to eliminate the denominators.
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Simplify the equation by distributing and combining like terms.
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Rearrange the equation to isolate the variable x.
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Solve for x by applying the appropriate algebraic operations.
The detailed solution is as follows:
Step 1: Multiply both sides by (x+2)(x-2): (x+2)(x-2) * [(2x) / (x+2) - 2] = (x+2)(x-2) * [(x-8) / (x-2)]
Step 2: Simplify the equation: 2x(x-2) - 2(x+2)(x-2) = (x-8)(x+2)
Step 3: Expand and simplify: 2x^2 - 4x - 2(x^2 - 4) = x^2 - 6x - 16
Step 4: Continue simplifying: 2x^2 - 4x - 2x^2 + 8 = x^2 - 6x - 16
Step 5: Combine like terms: -4x + 8 = -6x - 16
Step 6: Move all terms involving x to one side: -4x + 6x = -16 - 8
Step 7: Simplify: 2x = -24
Step 8: Solve for x by dividing both sides by 2: x = -12
Therefore, the solution to the equation (2x) / (x+2) - 2 = (x-8) / (x-2) is x = -12.
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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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