How do you solve #(5k + 5)/(3k^2) = (k  4)/(3k^2) + 1/k^2# and find any extraneous solutions?
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To solve the equation (5k + 5)/(3k^2) = (k  4)/(3k^2) + 1/k^2 and find any extraneous solutions, we can follow these steps:

Multiply both sides of the equation by 3k^2 to eliminate the denominators: (5k + 5) = (k  4) + 3k^2/k^2

Simplify the equation: 5k + 5 = k  4 + 3

Combine like terms: 5k + 5 = k  1 + 3

Simplify further: 5k + 5 = k + 2

Subtract k from both sides: 4k + 5 = 2

Subtract 5 from both sides: 4k = 3

Divide both sides by 4: k = 3/4
Therefore, the solution to the equation is k = 3/4. To check for extraneous solutions, substitute this value back into the original equation and verify if it holds true.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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