To solve this equation, we need to find a common denominator for both fractions:
(3x+1)/(x+2) = (2x-3)/(x-2)
First, we cross multiply to get rid of the fractions:
(x+2)(2x-3) = (x-2)(3x+1)
Expand both sides:
2x^2 - 3x + 4x - 6 = 3x^2 - 2x + x - 2
Combine like terms:
2x^2 + x - 6 = 3x^2 - x - 2
Rearrange the equation to set it to zero:
0 = 3x^2 - 2x - 2x^2 + x - 2 + 6
0 = x^2 - x + 4
Now, we will try to factor this quadratic equation. Since it cannot be factored, we can use the quadratic formula to find the values of x:
x = (-(-1) ± √((-1)^2 - 4(1)(4)))/(2(1))
x = (1 ± √(1 - 16))/2
x = (1 ± √(-15))/2
Since we have a negative value under the square root, the solutions are imaginary:
x = (1 ± √15i)/2
Therefore, the solution to the equation is x = (1 ± √15i)/2.
To solve this equation, we need to find a common denominator for both fractions:
(3x+1)/(x+2) = (2x-3)/(x-2)
First, we cross multiply to get rid of the fractions:
(x+2)(2x-3) = (x-2)(3x+1)
Expand both sides:
2x^2 - 3x + 4x - 6 = 3x^2 - 2x + x - 2
Combine like terms:
2x^2 + x - 6 = 3x^2 - x - 2
Rearrange the equation to set it to zero:
0 = 3x^2 - 2x - 2x^2 + x - 2 + 6
0 = x^2 - x + 4
Now, we will try to factor this quadratic equation. Since it cannot be factored, we can use the quadratic formula to find the values of x:
x = (-(-1) ± √((-1)^2 - 4(1)(4)))/(2(1))
x = (1 ± √(1 - 16))/2
x = (1 ± √(-15))/2
Since we have a negative value under the square root, the solutions are imaginary:
x = (1 ± √15i)/2
Therefore, the solution to the equation is x = (1 ± √15i)/2.