SOLUTION: For what value of x is the rational expression below equal to zero? x-1/(x-3)(x+1)

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Question 1027248: For what value of x is the rational expression below equal to zero?
x-1/(x-3)(x+1)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Expression as given or asked here,
x-1/(x-3)(x+1)

Appears when rendered,


Raise to equivalent in higher terms,





Your interest is now to find the REAL roots of the NUMERATOR. Start with synthetic division to check on the roots, -1, and 1, probably the only possible real roots but there MIGHT be irrational roots, also real. 


-1      |     1    -2    -3    -1
        |          -1    3     0
        |________________________________
             1     -3    0     -1          Not a root


1       |     1     -2     -3    -1
        |
        |            1     -1    -4
        |________________________________
             1      -1     -4     -5       Not a root

Use any other methods you know. You could try a graphing tool.


This appears to show two real roots but they are irrational. This seems strange.

Try a closer look:

Only ONE Real, irrational root, and it is slightly greater than 3.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

For what value of x is the rational expression below equal to zero?
x-1/(x-3)(x+1)
 

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