1/(1-x)(2-x) -2/(x-1)(x-3) -3/(x-2)(3-x)

asked by guest
on Jan 10, 2025 at 10:28 pm



You asked:

Evaluate the expression: \(\frac{1}{\left(1 - x\right) \left(2 - x\right)} - \frac{2}{\left(x - 1\right) \left(x - 3\right)} - \frac{3}{\left(x - 2\right) \left(3 - x\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{1}{\left(1 - x\right) \left(2 - x\right)} - \frac{2}{\left(x - 1\right) \left(x - 3\right)} - \frac{3}{\left(x - 2\right) \left(3 - x\right)} = - \frac{2}{\left(x - 3\right) \left(x - 1\right)} - \frac{3}{\left(3 - x\right) \left(x - 2\right)} + \frac{1}{\left(1 - x\right) \left(2 - x\right)} \)

Expanded

\[\frac{1}{\left(1 - x\right) \left(2 - x\right)} - \frac{2}{\left(x - 1\right) \left(x - 3\right)} - \frac{3}{\left(x - 2\right) \left(3 - x\right)} = \frac{1}{x^{2} - 3 x + 2} - \frac{2}{x^{2} - 4 x + 3} - \frac{3}{- x^{2} + 5 x - 6}\]

Factored

\[\frac{1}{\left(1 - x\right) \left(2 - x\right)} - \frac{2}{\left(x - 1\right) \left(x - 3\right)} - \frac{3}{\left(x - 2\right) \left(3 - x\right)} = \frac{2}{\left(x - 3\right) \left(x - 2\right)}\]

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