Why is a/(as+1) equivalent to 1/(s+1/a)?

[tranceical]

Hi guys,

please could someone tell me how this is equivalent and/or what the algebraic rule is?

how is this: a/as + 1

is equivalent to this: 1/s+1/a

Thanks a lot for your time and help

 

[ME_student]

So a/as=1/s do you agree?

 

[Mark44]

Hi guys,

please could someone tell me how this is equivalent and/or what the algebraic rule is?

how is this: a/as + 1

is equivalent to this: 1/s+1/a

First off, what you wrote is ambiguous. Taken literally, what you wrote is $\frac{a}{a}s + 1 = s + 1$, if a ≠ 0.

Assuming that's not what you meant, it could be either
$\frac{a}{as} + 1$
or $\frac{a}{as + 1}$

Starting with 1/s + 1/a, the rule for adding fractions says that we need a common denominator, so
1/s + 1/a = a/(as) + s/(as) = (a + s)/(as). This doesn't match any interpretations of what you wrote, so I don't see that what you started with is equal to 1/a + 1/s.

 

[tranceical]

Thanks for the replies. Sorry for the ambiguity i should have used parentheses.

Mark44 - What i meant: how is a/(as+1) equivalent to 1/(s+(1/a))

Me_student - i understand a/as=1/s but i don't understand how the other
terms equal? i.e. how does the +1 term from a/(as+1) become 1/a?

many thanks

 

[Mark44]

Thanks for the replies. Sorry for the ambiguity i should have used parentheses.

Mark44 - What i meant: how is a/(as+1) equivalent to 1/(s+(1/a))

a/(as + 1) = a/[a(s + 1/a)]
Can you finish it and show that the last expression is equal to 1/(s + 1/a)?
What I did was factor a from both terms in the denominator.

Me_student - i understand a/as=1/s but i don't understand how the other
terms equal? i.e. how does the +1 term from a/(as+1) become 1/a?

I explained that above.

 

[tranceical]

Thanks a lot Mark44 you've made that perfectly clear to me, i can see how the expressions equal now. Much appreciated :)