How do you solve the equation and identify any extraneous solutions for #1/(x1) + 4/(4x4) = 2#?
Extraneous would be if one of the numerator would be
In both fractions that means
And this is allowed.
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To solve the equation 1/(x1) + 4/(4x4) = 2 and identify any extraneous solutions, we can follow these steps:

Start by finding a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (x1)(4x4).

Multiply each term by the common denominator to eliminate the fractions. This gives us (4x4) + 4(x1) = 2(x1)(4x4).

Simplify the equation by distributing and combining like terms. This results in 4x  4 + 4x  4 = 8x^2  8x  8.

Combine like terms again to get 8x  8 = 8x^2  8x  8.

Move all terms to one side of the equation to obtain 8x^2  16x = 0.

Factor out the greatest common factor, which is 8x, to get 8x(x  2) = 0.

Set each factor equal to zero and solve for x. This gives us two possible solutions: x = 0 and x = 2.

Check each solution by substituting them back into the original equation. For x = 0, the original equation becomes 1/(1) + 4/(4) = 2, which simplifies to 1  1 = 2. This is not true, so x = 0 is an extraneous solution.

For x = 2, the original equation becomes 1/(21) + 4/(4(2)4) = 2, which simplifies to 1/1 + 4/4 = 2. This is true, so x = 2 is the only valid solution.
Therefore, the solution to the equation 1/(x1) + 4/(4x4) = 2 is x = 2, and there are no extraneous solutions.
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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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