Question

What is the quotient in simplified form? State any restrictions on the variable. Show Work.

Answer 1

a+2 a +1
= ------- / ------------------
a -5 (a - 3)(a - 5)

a+2 (a - 3)(a - 5)
= ------- * ------------------
a -5 a +1

(a+2)(a - 3)
= ----------------
a +1

a NOT equal 5 and -1

Answer 2

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))=(a^2-a-6)/(a+1)`

Restriction:

`a\\eq -1`

`a\\eq 5`

Explanation:

we are given

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))`

Since, it is division

so, we can flip it to get in multiplication

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))=((a+2)* (a^2-8a+15))/((a-5)* (a+1))`

now, we can factor it

and then we can simplify it

`a^2-8a+15=(a-5)(a-3)`

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))=((a+2)* (a-5)* (a-3))/((a-5)* (a+1))`

now, we can cancel it

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))=((a+2)* (a-3))/((a+1))`

`((a+2))/((a-5)) /((a+1))/((a^2-8a+15))=(a^2-a-6)/(a+1)`

Restriction:

we know that denominator can not be zero

so,

`a+1\\eq 0`

`a\\eq -1`

and factored term can not be 0 as well

`a-5\\eq 0`

`a\\eq 5`