i think i do something wrong again(2x+1)/(x-3)-(4x-1)/(2x-3) = 0
(2x-3)(2x+1)-(4x-1) = (0)(x-3)(2x-3)
4x^2+2x-6x-3-4x-1 = 2x^2-3x-6x+9
4x^2-4 = 2x^2-3x-6x+9
-2x^2-9x+13
i put this in quadratic formula and i think it wrong becaue i get 9/2 and 0for x and it have to be 2/3.
Your first line should have been
(2x-3)(2x+1)-(4x-1)(x-3) = (0)(x-3)(2x-3)
4x^2 - 4x - 3 - (4x^2 -13x + 3) = 0
4x^2 - 4x - 3 - 4x^2 + 13x - 3 = 0
9x = 6
x = 6/9 = 2/3
thank you very much reiny :)
To help you identify where the mistake occurred, let's go through the steps of solving the equation.
Here's the given equation:
(2x+1)/(x-3) - (4x-1)/(2x-3) = 0
Step 1: Find a common denominator for the fractions.
The common denominator in this case is (x-3)(2x-3). Multiply each fraction by the appropriate factor to obtain the common denominator:
[(2x+1)(2x-3)]/[(x-3)(2x-3)] - [(4x-1)(x-3)]/[(x-3)(2x-3)] = 0
Step 2: Simplify the numerators.
(4x^2-6x+2x-3) / [(x-3)(2x-3)] - (4x^2-12x-x+3) / [(x-3)(2x-3)] = 0
Step 3: Combine like terms in the numerators.
(4x^2-4x-3) / [(x-3)(2x-3)] - (4x^2-13x+3) / [(x-3)(2x-3)] = 0
Step 4: Subtract the fractions.
[(4x^2-4x-3) - (4x^2-13x+3)] / [(x-3)(2x-3)] = 0
Step 5: Simplify further.
[(4x^2-4x-3-4x^2+13x-3)] / [(x-3)(2x-3)] = 0
Step 6: Combine like terms in the numerator.
(9x-9) / [(x-3)(2x-3)] = 0
Step 7: Multiply both sides of the equation by the common denominator to eliminate it.
9x-9 = 0
Step 8: Solve for x.
Adding 9 to both sides of the equation:
9x = 9
Dividing both sides by 9:
x = 1
Therefore, according to the correct steps, the solution to the equation is x = 1. It seems there was an error in your initial calculations.