# Algebra equivalence help

by tranceical
Tags: algebra, equivalence
 P: 20 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
 P: 61 So a/as=1/s do you agree?
Mentor
P: 21,311
 Quote by 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
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.

 P: 20 Algebra equivalence help 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 dont understand how the other terms equal? i.e. how does the +1 term from a/(as+1) become 1/a? many thanks
Mentor
P: 21,311
 Quote by 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))
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.
 Quote by tranceical Me_student - i understand a/as=1/s but i dont understand how the other terms equal? i.e. how does the +1 term from a/(as+1) become 1/a?
I explained that above.
 P: 20 Thanks a lot Mark44 you've made that perfectly clear to me, i can see how the expressions equal now. Much appreciated :)

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