Divide[3x,x-2]+ Divide[2Power[x,2]-5,4-Power[x,2]]-Divide[x-1,x+2]

asked by guest
on Nov 15, 2024 at 6:32 am



You asked:

Evaluate the expression: \(\frac{3 x}{x - 2} + \frac{2 \cdot {x}^{2} - 5}{4 - {x}^{2}} - \frac{x - 1}{x + 2}\)

MathBot Answer:

Evaluated



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


Expanded

\[\frac{3 x}{x - 2} + \frac{2 \cdot {x}^{2} - 5}{4 - {x}^{2}} - \frac{x - 1}{x + 2} = \frac{2 x^{2}}{4 - x^{2}} - \frac{x}{x + 2} + \frac{3 x}{x - 2} + \frac{1}{x + 2} - \frac{5}{4 - x^{2}}\]


Factored

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