The solution to the equation [tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex] is (b) there is no solution.
How to solve the rational equation?
The equation is given as:
[tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex]
Factorize the quadratic numerator
[tex]\frac{2x}{x - 1} - \frac{2x -5}{(x - 1)(x - 2)} = \frac{-3}{x -2}[/tex]
Multiply through by (x - 1)(x - 2)
2x(x - 2) - (2x -5) = -3(x - 1)
Expand
2x² - 4x - 2x + 5 = -3x + 3
Collect like terms
2x² - 4x - 2x + 3x + 5 - 3 = 0
Evaluate the like terms
2x² - 3x + 2 = 0
Using a graphical tool, the above equation has no real solution
Hence, the solution is (b) there is no solution.
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