SOLUTION: solve this equation by using the quadratic form 3/x-7+4/x+2=1

The other tutor took your equation to be



because you didn't put parentheses around denominators to show
where they start and where they end.  When you write algebra 
fractions all on one line, using a foward slash "/" for a fraction
bar, you must put parentheses around both entire numerators and
entire denominators any time there is more than just one letter 
or just one number in the numerator or denominator.  Otherwise
there is no way to know where numerators and denominators start 
and end.  And when you don't put the parentheses in, it is 
understood that the numerator or denominator consists of just 
the one number or the one letter which is closest to the forward 
slash "/".  That's the way the other tutor interpreted your
equation.

I believe you intended for your equation to be this:



which you should have written all on one line as

3/(x-7)+4/(x+2)=1

That way we can tell that the -7 and +2 are parts of the 
denominators and not separate terms.  It was not necessary
to place parentheses around the numerators because they
just consist of one number each, 3 and 4, but it was necessary 
to put parentheses around the denominators.

Assuming you meant this:

,

write the 1 as  so everything will be a fraction:



The LCD is (x-7)(x+2) so we multiply through by   




Then we cancel away the denominators:



We end up with no fractions at all



Remove the parentheses:



Collect like terms:



Get 0 on the left:



Swap sides:



Compare to 



And see that a=1, b=-12 and c=8.

Then use

 

 



 





Factor 4 out of the top:



Divide top and bottom by 2



or if you prefer:



The two exact solutions are

 and 

They are approximately 0.7 and 11.3.

Edwin