SOLUTION: Rational Equation 3/x+1-4=5/x-2

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Question 1208188: Rational Equation
3/x+1-4=5/x-2

Found 3 solutions by ikleyn, josgarithmetic, mccravyedwin:
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.

Look how your post appears at the forum.

As it is written, it CONTRADICTS to the rules of writing mathematical expressions for rational functions.

Use parentheses to show which part of the formula is the denominator and which is the numerator (where it is required).


Without it, your writing/equation is UNREADABLE.



Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean exactly what you write?
3/x+1-4=5/x-2
3%2Fx%2B1-4=5%2Fx-2

-3=2%2Fx-2
-1=2%2Fx
1%2Fx=-1%2F2
x=-2

Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!

It is very hard to teach students to type mathematical expressions all on one
line.  They will invariably fail to enclose numerators and denominators
(especially denominators) that contain more than just one number or just one
letter in parentheses.

But obviously no teacher teaching fractional equations would be testing to see
if a student at that level would be able to do such a simple thing as to
combine +1 and -4. 

So no doubt they meant this:

3/(x+1)-4=5/(x-2)  when typed all on one line.

3%2F%28x%2B1%29-4=5%2F%28x-2%29

Multiply through by LCD (x+1)(x-2)





3%28x-2%29-4%28x%2B1%29%28x-2%29=5%28x%2B1%29

3x-6-4%28x%5E2-x-2%29=5x%2B5%29

3x-6-4x%5E2%2B4x%2B8=5x%2B5%29

-4x%5E2%2B7x%2B2=5x%2B5

-4x%5E2%2B2x-3=0

4x%5E2-2x%2B3=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%2A%284%29%2A%283%29+%29%29%2F%282%2A%284%29%29+

x+=+%282+%2B-+sqrt%284-48+%29%29%2F8+

x+=+%282+%2B-+sqrt%28-44+%29%29%2F8+

x+=+%282+%2B-+i%2Asqrt%284%2A11+%29%29%2F8+

x+=+%282+%2B-+2i%2Asqrt%2811+%29%29%2F8+

x+=+%282%281+%2B-+i%2Asqrt%2811+%29%29%29%2F8+

x+=+%281+%2B-+i%2Asqrt%2811+%29%29%2F4+

Edwin