Question

How would I factor it when I have the fraction in it

Answer 1

The given expression is

`(x-(1)/(x))^3`

According to Pascal's Triangle, the third row is 1 3 3 1.

This means the binomial expansions must have 4 terms, where each number belongs to each of them as a coefficient.

Now, the binomial expansion would be

`(x-(1)/(x))^3=x^3+3x^2(-(1)/(x))+3x(-(1)/(x))^2+(-(1)/(x))^3`

Now, we need to solve each parenthesis using the distributive property.

`x^3-(3x^2)/(x)+(3x)/(x^2)-(1)/(x^3)`

Then, we simplify variables, remember that division of powers is solved by subtracting exponents

`x^3-3x^(2-1)+3x^(1-2)-(1)/(x^3)=x^3-3x+3x^(-1)-(1)/(x^3)`

At last, we place the negative power as denominator

`x^3-3x+(3)/(x)-(1)/(x^3)`