SOLUTION: -3 over 4 S - 3 = 1 over 3 S + 1 over 4

Question 160217: -3 over 4 S - 3 = 1 over 3 S + 1 over 4
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
(-3/4s) - (3/1) = 1/(3s) + 1/4

Here is the correct set up equation:

(-3/4S) - 3/1 = (1/3S) + 1/4

I needed to put parentheses for easy reading. Any number or letter by itself = that number or letter over 1.
So, -3 is really -3/1 but we never write this way except in math courses.

Back to your question.

I will solve for S and let you prove it.

(-3 - 4(4S))/4S = 7/12S

(-3 -12S)/4S = 7/12S

We now cross-multiply.

4S times 7 = (12S) times the quantity (-3 - 12S)

28S = -36S - 144S^2

Set everything to zero.

144S^2 + 36S - 28S = 0

144S^2 + 8S = 0

Factor out 8S.

8S(18S + 1) = 0

We now have two factors:

8S and the quantity (18S + 1)

Set each factor to zero and solve for S.

8S = 0

S = 0/8

S = 0

Next factor:

18S + 1 = 0

18S = -1

S = -1/18

We have two answers for S, but which one is the right one?

To find out, replace S in your original fractional equation given with 0 and simplify and then replace S again
with -1/18 and simplify.

Whichever value for S gives you the same answer on both sides of the equation, that will be your correct value for S.

Don't be surprised if BOTH S = 0 and S = -1/18 are correct.

I will let you plug and chug.

If you cannot do this, write back but please try on your own first. I did most of the work in your place.

midwood_trail

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