Why can't I separate the fraction inside a fraction to the outsideI know when I have something of this form a 1 α s + 1 T s + 1 α T I multiply out the fractional part, α with the bottom to get a s + 1 T α s + 1 T But, if I instead have a 1 α ( s + 1 T ) s + 1 α T with the fractional part 1 α in the numerator instead.I know I can't take the fractional part out of the equation in this second instance. But, I don't know why that is. I know this is a fairly basic rule, but I haven't done algebra in quite a while. So, I wanted to ask for clarification.

Question

Why can&#039;t I separate the fraction inside a fraction to the outsideI know when I have something of this form      a        1    α              s      +              1        T                    s      +              1                  α          T                    I multiply out the fractional part, α with the bottom to get      a              s      +              1        T                    α      s      +              1        T            But, if I instead have      a                      1        α            (      s      +              1        T            )              s      +              1                  α          T                    with the fractional part      1    α  in the numerator instead.I know I can&#039;t take the fractional part out of the equation in this second instance. But, I don&#039;t know why that is. I know this is a fairly basic rule, but I haven&#039;t done algebra in quite a while. So, I wanted to ask for clarification.

lefeuilleton42 · Accepted Answer

I know I can&#039;t take the fractional part out of the equation in this second instanceWhat? Yes you can. (Technically it&#039;s &quot;expression&quot; and not &quot;equation.&quot;)In general,                     A        B            C        =  A            B      C      , as long as   C  ≠  0 since otherwise these expressions are undefined.In your case:  a                       1        α            (      s      +              1        T            )              s      +              1                  α          T                      =  a         1    α              s      +              1        T                    s      +              1                  α          T

Why can't I separate the fraction inside a fraction to the outside. I know when I have something of this form a 1/(alpha) (s + 1/T)/(s + 1/(alpha T))

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