Question

Multiply or Divide the rational expression (m²+9m+14)/(m+2)*(9)/(m²+5m-14)

Answer 1

To simplify the given rational expression, factor the quadratic expressions and cancel out common factors in the numerator and denominator, resulting in the simplified expression 9/(m-2).

Step-by-step explanation:

The task is to multiply or divide the rational expression (m²+9m+14)/(m+2)*(9)/(m²+5m-14) by simplifying and canceling common factors where possible.

Begin by factoring the quadratic expressions if possible:

1. 
   
3. Factor m²+9m+14 to (m+7)(m+2).
4. 
   
6. Factor m²+5m-14 to (m+7)(m-2).

After factoring, the expression looks like this:

((m+7)(m+2))/(m+2) * 9/((m+7)(m-2))

Next, cancel out the common factors in the numerator and denominator:

((cancel(m+7))(cancel(m+2)))/(cancel(m+2)) * 9/(cancel(m+7))(m-2)

Now, you are left with:

1 * 9/(m-2) = 9/(m-2)

So, the simplified rational expression is 9/(m-2).

Remember, when multiplying fractions, you multiply the numerators together and multiply the denominators together, simplifying by common factors as needed. If there was any division, we would follow the rule of inverting the divisor and then multiplying. We also make sure that we perform the same operations to both sides of an equation to maintain equality.