easy probelm?

Question

Mind boggled math probelm

solve for R

1/R = 1/a + 1/b + 1/c

is it R=abc or
R = 1/abc or R = 1/ 1/abc

Answer 1

Needs a few more steps.

Eventually you want to be able to "invert" (or turn over ) the right hand side

First you need to make it into a single term (some numbers over a SINGLE LONG LINE over some numbers.

You need the common denominator....here we go off track in square brackets for a number example.

[1/3 + 1/4 + 1/6.......the common denominator is the smallest number that 3,4 and 6 will all go into. Choose 12 for the common denominator.

you say 3 into 12 goes 4; 4 times 1 = 4 so write 4 + in the numerator

You say 4 into 12 goes 3; 3 times 1 = 3 so write 3 + in the numerator

lastly 6 into 12 goes 2; 2 x 1 = 2

so the finished numerator is (4 + 3 + 2) all over 12

=9/12


if you were going to invert this you'd finish up with 12/9]


Now back to your question with a,b,c

The lowest common denominator = abc (a times b times c)

a goes into abc bc times; bc times 1 = bc

similarly

b goes into abc ac times; ac times 1 = ac

and

c goes into abc ab times; ab times 1 = ab

1/R = (bc + ac + ab)/abc

therefore

R = abc/ (bc + ac + ab).

Answer 2

None of those. Here's how it works:

You need to combine the fractions on the right side of the equation, which requires you to have an LCD (lowest common denominator). In this case, that would be abc, since we have no way of factoring variables. Changing each fraction to have that denominator, you end up with:
1/R = bc/abc + ac/abc + ab/abc
Simplify that to:
1/R = (ab + ac + bc)/abc
Take the reciprocal to get:
R = abc/(ab + ac + bc)
Unfortunately, there's no way to simplify it past that.

Answer 3

Actually, it's none of the above!
Combine the 3 fractions:
Their LCD is abc,
so their sum is
(ab + ac + bc)/abc = 1/R.
Now flip both sides to get
R = abc/(ab + ac + bc).
Hope that helps!

Answer 4

multiply by R (both side naturally)

1=R(1/a+1/b+1/c)

R= 1/(1/a+1/b+1/c)

multiply by abc (the right had side both the upper and lower part

R= abc/(bc+ac+ab)


all your options in your question are incorrect

Answer 5

Well, here we go:

(1/R) = (1/a) + (1/b) + (1/c)
(1/R) = (a + b + c)/(abc)

R = (abc)/(a+b+c)

Answer 6

R is the reciprocal of 1/R

Therefore, R = 1 / [(1/a)+(1/b)+(1/c)]

Answer 7

1/R = 1/a + 1/b + 1/c
= bc/abc + ac/abc + ab/abc
=(ab + ac + bc)/(abc)
Thus R = (abc)/(ab + ac + bc)

Answer 8

1/R=1/a+1/b+1/c
=[bc+ca+ab]/abc
R=abc/[ab+bc+ca]