Factorising this formulaI came across this simplification in an iTunes U calculus course. 1 x 0 + δ x − 1 x 0 δ x = 1 δ x ( x 0 − ( x 0 + δ x ) ( x 0 + δ x ) x 0 ) I didn't understand how this was done. I can see the denominator being taken out for 1 δ x but do not understand the remainder. Can someone give me some guidance? Thanks

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Factorising this formulaI came across this simplification in an iTunes U calculus course.                    1                              x                          0                                +          δ          x                    −              1                  x                      0                                      δ      x        =      1          δ      x            (                            x                      0                          −        (                  x                      0                          +        δ        x        )                    (                  x          0                +        δ        x        )                  x                      0                                )  I didn&#039;t understand how this was done. I can see the denominator being taken out for       1          δ      x       but do not understand the remainder. Can someone give me some guidance? Thanks

Giovani Hickman · Accepted Answer

It is      1    a    −      1    b    =            b      −      a              a      b        .So, if   a  =      x    0    +  δ  x and   b  =      x    0   you have      1                  x        0            +      δ      x        −      1          x      0        =                    x        0            −      (              x        0            +      δ      x      )                      x        0            (              x        0            +      δ      x      )        .

prensistath · Accepted Answer

Basically it is taking the same denominator:      1    a    −      1    b    =      b          a      b        −      a          a      b        =            a      −      b              a      b        .In the special case   a  =      x    0  ,   b  =      x    0    +  δ  x

Factorising this formula I came across this simplification in an iTunes U calculus course.

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