How do you solve #2/(x1)  2/3 =4/(x+1)#?
This results in a more straightforward equation after the denominators are cancelled.
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To solve the equation 2/(x1)  2/3 = 4/(x+1), we can follow these steps:

Multiply every term in the equation by the least common denominator (LCD) of (x1), 3, and (x+1), which is 3(x1)(x+1). This step eliminates the denominators.

Simplify the equation by distributing and combining like terms.

Solve for x by isolating the variable on one side of the equation.
Here are the steps in detail:

Multiply every term by the LCD, 3(x1)(x+1):
3(x1)(x+1) * [2/(x1)  2/3] = 3(x1)(x+1) * 4/(x+1)
Simplifying the left side: 3(x1)(x+1) * 2/(x1)  3(x1)(x+1) * 2/3

Distribute and combine like terms:
6(x+1)  2(x1)(x+1) = 12(x1)
Simplifying further: 6x + 6  2(x^2  1) = 12x  12

Simplify and solve for x:
6x + 6  2x^2 + 2 = 12x  12
Rearranging the terms: 2x^2 + 6x + 8 = 12x  12
Combining like terms: 2x^2  6x + 12x = 12  8
Simplifying further: 2x^2 + 6x = 20
Rearranging the terms: 2x^2  6x + 20 = 0
Factoring the quadratic equation is not possible, so we can use the quadratic formula:
x = (b ± √(b^2  4ac)) / (2a)
Plugging in the values: x = ((6) ± √((6)^2  4(2)(20))) / (2(2))
Simplifying: x = (6 ± √(36  160)) / 4
x = (6 ± √(124)) / 4
Since the square root of a negative number is not a real number, this equation has no real 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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