Question

Please simplify the following with steps, thank you..
((x^4)-1)/(x-1)

Answer 1

The top is a difference of squares
\[a^2-b^2=(a+b)*(a-b)\]

Answer 2

\[\frac{(x^4-1)}{(x-1)}=\frac{ ((x^2)^2-1^2 }{ x-1}=\frac{ (x^2+1)*(x^2-1) }{ x-1 }\]

Answer 3

then we have a new difference of squares, again in the numerator

Answer 4

\[x^2-1^2=(x+1)*(x-1)\]

Answer 5

this makes the equation become
\[\frac{(x^2+1)∗(x^2−1^2)}{x−1}=\frac{ (x^2+1)*(x+1)*(x-1) }{ (x-1) }\]

Answer 6

Last step is the cancel out the same binomials from the top and bottom of the fraction

Answer 7

(x2+1)∗(x+1)

Answer 8

Thank you