Question

Solve the rational equation:

Answer 1

The solution to the equation $\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}$ is (b) there is no solution.

How to solve the rational equation?

The equation is given as:

$\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}$

Factorize the quadratic numerator

$\frac{2x}{x - 1} - \frac{2x -5}{(x - 1)(x - 2)} = \frac{-3}{x -2}$

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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brainly.com/question/1851758

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