How do you simplify and restricted value of #(a^2 - a - 2)/(a^2 - 13a + 30)#?

1 Answer
May 19, 2017

Answer:

#frac((a + 1)(a - 2))((a - 3)(a - 10))#; #a ne 3, 10#

Explanation:

We have: #frac(a^(2) - a - 2)(a^(2) - 13 a + 30)#

Let's factorise both the numerator and the denominator using the "middle-term break":

#= frac(a^(2) + a - 2 a - 2)(a^(2) - 3 a - 10 a + 30)#

#= frac(a(a + 1) - 2(a + 1))(a(a - 3) - 10(a - 3))#

#= frac((a + 1)(a - 2))((a - 3)(a - 10))#

Now let's evaluate the restricted values of #a#.

The denominator of the fraction can never be equal to zero:

#Rightarrow (a - 3)(a - 10) ne 0#

Using the null factor law:

#Rightarrow a - 3 ne 0, a - 10 ne 0#

#Rightarrow a ne 3, a ne 10#

#therefore frac(a^(2) - a - 2)(a^(2) - 13 a + 30) = frac((a + 1)(a - 2))((a - 3)(a - 10))#; #a ne 3, 10#