To solve this equation, we can simplify the expressions first.
The equation is: 3/(2x+3) - 1/(2x+1) = 1/(x+1)
First, we can find a common denominator for the fractions. In this case, the least common multiple of (2x+3) and (2x+1) is (2x+3)(2x+1).
Now, let's multiply all terms by the common denominator to eliminate the denominators:
(3/(2x+3)) * (2x+1) - (1/(2x+1)) * (2x+3) = (1/(x+1)) * (2x+1)(2x+3)
Simplifying, we get:
3(2x+1) - (2x+3) = (2x+1)(2x+3)
6x+3 - 2x-3 = 4x^2 + 6x + 2x + 3
Combining like terms, we have:
4x = 4x^2 + 8x + 3
Moving all terms to one side of the equation, we get:
4x^2 + 4x + 3 - 4x = 0
Simplifying further:
4x^2 + 3 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
The equation cannot be factored easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 0, and c = 3. Plugging in these values, we get:
x = (0 ± √(0^2 - 4(4)(3))) / (2(4))
= (0 ± √(0 - 48)) / 8
= (0 ± √(-48)) / 8
Taking the square root of a negative number gives us imaginary solutions.
Therefore, the equation 3/(2x+3) - 1/(2x+1) = 1/(x+1) does not have real solutions.
3÷2x+3 -1÷2x+1 =1÷x+1
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