The simplified form of the algebraic expression [tex]\frac{x+2}{x^{2} +5x+6} / \frac{3x+1}{x^{2} -9}\\[/tex] is [tex]\frac{x-3}{3x + 1}[/tex].
What is simplifying an algebraic expression?
Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
[tex]= \frac{x+2}{x^{2} +5x+6} / \frac{3x+1}{x^{2} -9}\\ \\ = \frac{x+2}{x^{2} +5x+6} * \frac{x^{2} -9}{3x+1}[/tex]
Solving in parts,
[tex]=x^{2} +5x + 6\\\\= x^{2} + 2x + 3x + 6\\\\=x(x+2) + 3(x+2)\\\\=(x+2)(x+3)[/tex]
[tex]= x^{2} -9\\\\= x^{2} - 3^{2}\\ \\=(x - 3)(x + 3)[/tex]
[tex]= \frac{x+2}{x^{2} +5x+6} * \frac{x^{2} -9}{3x+1}\\\\= \frac{x+2}{(x+2)(x+3)} * \frac{(x+3)(x-3)}{3x+1}\\ \\=\frac{x-3}{3x + 1}[/tex]
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