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

asked by guest
on Apr 02, 2025 at 8:12 pm



You asked:

Evaluate the expression: x+1x+3+2x−1x+2\frac{x + 1}{x + 3} + \frac{2 x - 1}{x + 2}

MathBot Answer:

Evaluated



x+1x+3+2x−1x+2=2x−1x+2+x+1x+3\displaystyle \frac{x + 1}{x + 3} + \frac{2 x - 1}{x + 2} = \frac{2 x - 1}{x + 2} + \frac{x + 1}{x + 3}

Expanded

x+1x+3+2x−1x+2=xx+3+2xx+2+1x+3−1x+2\frac{x + 1}{x + 3} + \frac{2 x - 1}{x + 2} = \frac{x}{x + 3} + \frac{2 x}{x + 2} + \frac{1}{x + 3} - \frac{1}{x + 2}

Factored

x+1x+3+2x−1x+2=3x2+8x−1(x+2)(x+3)\frac{x + 1}{x + 3} + \frac{2 x - 1}{x + 2} = \frac{3 x^{2} + 8 x - 1}{\left(x + 2\right) \left(x + 3\right)}

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