Kevin C. answered • 04/04/14
Tutor
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Successful Math Tutor -- Recently retired high school math teacher
First, find the Least Common Denominator. That is the polynomial that each of these divide into.
That would be 3x(x+4).
We now need to multiply each term by this: (3x(x+4))(1/x - 1/(x+4) = 1/3)
Note that this now becomes: 3x(x+4)/x - 3x(x+4)/(x+4) = 3x(x+4)/3.
Reduce the fractions: 3(x+4) - 3x = x(x+4).
Distribute: 3x+12-3x = x2+4x.
Combine terms: x2+4x-12 = 0.
Factor: (x-2)(x+6) = 0
So: x = 2, and -6.
I hope that explains the process.
Philip P.
tutor
As Kevin stated above, to add any fractions - even rational expressions - you have to put them over a common denominator.
1 1 1
--- + ------ = ---
x (x+4) 3
1 (x+4) 1 x 1
--- ------ - ------ --- = ---
x (x+4) (x+4) x 3
--- ------ - ------ --- = ---
x (x+4) (x+4) x 3
x + 4 - x 1
---------- = ---
(x+4)x 3
4 1
---------- = ---
(x2 + 4x) 3
12 = x2 + 4x
0 = x2 + 4x -12
Solve as Kevin showed you above.
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04/05/14
L O.
this was a big help now I understand
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04/05/14
Philip P.
tutor
I'm glad it helped. The thing to remember is that to add or subtract fractions, put them over a common denominator.
1 1
--- + ---
3 4
1 4 1 3
--- --- + --- ---
3 4 4 3
4 3 7
--- + --- = ---
12 12 12
This holds true for rational expressions, which are fractions.
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04/05/14
L O.
Appreciate the example
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04/05/14
L O.
04/05/14