Answer:
[tex] \frac{x + 5}{x - 4} [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 3x - 10}{ {x}^{2} - 6x + 8} [/tex]
First, we will factor the numerator.
[tex] \frac{ ({x}^{2} - 2x) + (5x - 10)}{ {x}^{2} - 6x + 8} [/tex]
[tex] \frac{ x(x - 2) + 5(x - 2)}{ {x}^{2} - 6x + 8} [/tex]
[tex] \frac{ (x - 2) (x + 5)}{ {x}^{2} - 6x + 8} [/tex]
Now, we factor the denominator.
[tex] \frac{ (x - 2) (x + 5)}{ ({x}^{2} - 2x)+ ( - 4x + 8)} [/tex]
[tex] \frac{ (x - 2) (x + 5)}{ x({x} - 2) - 4( x - 2)} [/tex]
[tex] \frac{ (x - 2) (x + 5)}{ ({x} - 2) (x - 4)} [/tex]
Cancel out common factor x-2:
[tex] \frac{x + 5}{x - 4} [/tex]
