Answer:
Simplify the expression: [tex]\frac{\frac{b^2+5b+6}{3bc}}{\frac{b^2-9}{6bc}}[/tex]
The top expression given in the above fraction is Numerator and the bottom expression is called Denominator.
Now, multiply the numerator and denominator by [tex]6bc[/tex] ;
[tex]\frac{6bc \cdot(\frac{b^2+5b+6}{3bc})}{6bc \cdot (\frac{b^2-9}{6bc})}[/tex]
Simplify:
[tex]\frac{b^2+5b+6}{b^2-9}}[/tex]
Now, Factor the numerator [tex]b^2+5b+6 = (b+3)(b+2)[/tex] and denominator [tex]b^2-9 = (b-3)(b+3)[/tex];
[tex]\frac{(b+3)(b+2)}{(b+3)(b-3)}}[/tex]
Now, cancel the common factor (b+3) we get;
[tex]\frac{(b+3)(b+2)}{(b+3)(b-3)}} = \frac{b+2}{b-3}[/tex]
Therefore, the simplify expression of [tex]\frac{\frac{b^2+5b+6}{3bc}}{\frac{b^2-9}{6bc}}[/tex] is, [tex]\frac{b+2}{b-3}[/tex]
