Question

Simplify the expression.

Answer 1

Simplify the expression:
`((b^2+5b+6)/(3bc))/((b^2-9)/(6bc))`

The top expression given in the above fraction is Numerator and the bottom expression is called Denominator.

Now, multiply the numerator and denominator by
`6bc` ;

`(6bc \cdot((b^2+5b+6)/(3bc)))/(6bc \cdot ((b^2-9)/(6bc)))`

Simplify:

`(b^2+5b+6)/(b^2-9)}`

Now, Factor the numerator
`b^2+5b+6 = (b+3)(b+2)` and denominator
`b^2-9 = (b-3)(b+3)`;

`((b+3)(b+2))/((b+3)(b-3))}`

Now, cancel the common factor (b+3) we get;

`((b+3)(b+2))/((b+3)(b-3))} = (b+2)/(b-3)`

Therefore, the simplify expression of
`((b^2+5b+6)/(3bc))/((b^2-9)/(6bc))` is,
`(b+2)/(b-3)`