SOLUTION: 7x+6/x+4=3x-10/x+4

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Question 249539: 7x+6/x+4=3x-10/x+4
Answer by chosenpoint(26) About Me  (Show Source):
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Exponents/249539 (2009-12-13 22:51:56): 7x+6/x+4=3x-10/x+4

This one is a bit tricky, but the answer may seem obvious at first:

7x%2B6%2Fx%2B4=3x-10%2Fx%2B4 given

7x%2B6x%5E-1%2B4=3x-10x%5E-1%2B4 put into exponent form

4x%2B6x%5E-1%2B4=-10x%5E-1%2B4subtract 3x from both sides

4x%2B16x%5E-1%2B4=4 add 10x%5E-1 to both sides

4x%2B16x%5E-1=0 subtract 4 from both sides

4x%2A%281%2B4x%5E-2%29=0 factor

4x=0simplify and break apart

x=0%2F4 divide both sides by 4

x=0 simplify

or

1%2B4x%5E-2=0 simplify and break apart

4x%5E-2=-1 subtract 1 from both sides

1%2Fx%5E2=-1%2F4 impossible, since no real number works for this expression due to the negative sign

The only possible root seems to be 0.

Final Answer: x=0