Question

Simplify the rational expression. State any restrictions on the variable.

\frac{q^2+11q+24}{q^2-5q-24}

Answer 1

Explanation:

The given rational expression is:

`(q^2+11q+24)/(q^2-5q-24)`

On solving the above expression, we get

=
`(q^2+8q+3q+24)/(q^2-8q+3q-24)`

=
`(q(q+8)+3(q+8))/(q(q-8)+3(q-8))`

=
`((q+3)(q+8))/((q+3)(q-8))`

=
`(q+8)/(q-8)`

which is the required simplified expression.

Answer 2

`Given \: \: expression \: \: - \\ \\ \frac{ {q}^(2) + 11q + 24 }{ {q}^(2) - 5q - 24 } \\ \\ \frac{ {q}^(2) + 8q + 3q + 24 }{ {q}^(2) - 8q + 3q- 24 } \\ \\ (q(q + 8) + 3(q + 8))/(q(q - 8) + 3(q - 8)) \\ \\ ((q + 3)(q + 8))/((q + 3)(q - 8)) \\ \\ \\\: \: \: \: \: \: \: ((q + 8))/((q - 8)) \: \: \: \: \: \: \: \: \: \: \: \: Ans.\\ \\ (Where\: q \:is\: not\: equal \:to \:8)`