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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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