Answer:
[tex] \frac{2x - 5}{x + 5} [/tex]
Step-by-step explanation:
Firstly, you have to factorize the expressions on the numerator and denorminator :
Numerator :
[tex]2 {x}^{2} - 3x - 5[/tex]
[tex] = 2 {x}^{2} + 2x - 5x - 5[/tex]
[tex] = 2x(x + 1) - 5(x + 1)[/tex]
[tex] = (2x - 5)(x + 1)[/tex]
Denorminator :
[tex] {x}^{2} + 6x + 5[/tex]
[tex] = {x}^{2} + x + 5x + 5[/tex]
[tex] = x(x + 1) + 5(x + 1)[/tex]
[tex] = (x + 1)(x + 5)[/tex]
Next, you have to put the factorized-form in the fraction and cut out the similar expressions :
[tex] \frac{(2x - 5)(x + 1)}{(x + 1)(x + 5)} [/tex]
[tex] = \frac{2x - 5}{x + 5} [/tex]
