** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** Specify the solving method

**

**

Find the roots of the polynomial $\frac{x^2+x-2}{x^2+5x+6}$ by putting it in the form of an equation and then set it equal to zero

**

**

Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$

**

**

Thus

**

**

Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$

**

**

Thus

**

**

Simplifying

**

**

Multiply both sides of the equation by $x+3$

**

**

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-1$ from both sides of the equation

**

**

Multiply $-1$ times $-1$

**

**

Multiply $-1$ times $-1$

Verify that the solutions obtained are valid in the initial equation

**

**

The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed

** Final Answer

**