Question

Select the exclusion that fits best with this problem. a^3-b^3 / a^3b^3+a^2b^4+ab^5

Answer 1

Given the expression:

`(a^3-b^3)/(a^3b^3+a^2b^4+ab^5)`

You need to remember that a fraction with a denominator zero is not defined. Therefore, you must exclude all those values that make the denominator of the expression zero. To do this, you must find those values:

1. Make the denominator equal to zero:

`a^3b^3+a^2b^4+ab^5=0`

2. Factor it by factoring the Greatest Common Factor (GDF) out of the expression. Knowing that the Greatest Common Factor is the largest factor all the terms have in common, you can identify that, in this case:

`GCF=ab^3`

Then:

`ab^3(a^2+ab+b^2)=0`

3. Notice that you can split it as:

`ab^3=0`

And:

`a^2+ab+b^2=0`

Therefore, the exclusion is:

`a,b=0`

`a^2+ab+b^2=0`

Hence, the answer is: Last option.