(3d-2)/(d^2-3d+2) - (3d-1)/(d^2-2d)

asked by guest
on Sep 23, 2024 at 2:08 am



You asked:

Evaluate the expression: \(\frac{3 d - 2}{{d}^{2} - 3 d + 2} - \frac{3 d - 1}{{d}^{2} - 2 d}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{3 d - 2}{{d}^{2} - 3 d + 2} - \frac{3 d - 1}{{d}^{2} - 2 d} = \frac{3 d - 2}{d^{2} - 3 d + 2} - \frac{3 d - 1}{d^{2} - 2 d} \)

Expanded

\[\frac{3 d - 2}{{d}^{2} - 3 d + 2} - \frac{3 d - 1}{{d}^{2} - 2 d} = \frac{3 d}{d^{2} - 3 d + 2} - \frac{3 d}{d^{2} - 2 d} - \frac{2}{d^{2} - 3 d + 2} + \frac{1}{d^{2} - 2 d}\]

Factored

\[\frac{3 d - 2}{{d}^{2} - 3 d + 2} - \frac{3 d - 1}{{d}^{2} - 2 d} = \frac{2 d - 1}{d \left(d - 2\right) \left(d - 1\right)}\]

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