** Final Answer

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** Step-by-step Solution **

** Specify the solving method

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Find the roots of the equation using the Quadratic Formula

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

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Thus

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

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Thus

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Simplifying

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

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

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Canceling terms on both sides

Verify that the solutions obtained are valid in the initial equation

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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

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