Question

What is the simplified form of x minus 5 over x squared minus 3x minus 10 ⋅ x plus 4 over x squared plus x minus 12?

Answer 1

Answer:

$\frac{2x - 1}{ {x}^{2} - x - 6 }$

Step-by-step explanation:

$\frac{x - 5}{ {x}^{2} - 3x - 10 } + \frac{x + 4}{ {x}^{2} + x - 1 } \\ \frac{x - 5}{(x - 5)(x + 2)} + \frac{x + 4}{(x + 4)(x - 3)} \\ \frac{1}{x + 2} + \frac{1}{x - 3} = \frac{x - 3 + x + 2}{(x + 2)(x - 3)} \\ = \frac{2x - 1}{ {x}^{2} - x - 6 }$