Question

D" id="TexFormula1" title="\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}" alt="\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}" align="absmiddle" class="latex-formula">

Answer 1

The value of x in the equation $\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}$ is x = -1 or x = -2

How to solve the equation?

The equation is given as:

$\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}$

Start by taking the LCM

$\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}$

Expand the denominator

$\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}$

Cancel out the common factor

4x(x - 2) - 5x(x - 1)= 2

Expand

$4x^2 - 8x - 5x^2 + 5x = 2$

Evaluate the like terms

$-x^2 - 3x = 2$

Rewrite as:

$x^2 + 3x + 2 = 0$

Expand

$x^2 + 2x + x + 2 = 0$

Factorize

x(x + 2) + 1(x + 2) = 0

Factor out x + 2

(x + 1)(x + 2) = 0

Solve for x

x = -1 or x = -2

Hence, the value of x in the equation $\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}$ is x = -1 or x = -2

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brainly.com/question/1851758

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