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