SOLUTION: #46 Solve for x 3/x+1=3/x-1 I just can't seem to get this one to work out. I think the answer is x^2-x-3=0 Thanks for your help.

Algebra ->  Functions -> SOLUTION: #46 Solve for x 3/x+1=3/x-1 I just can't seem to get this one to work out. I think the answer is x^2-x-3=0 Thanks for your help.      Log On


   

Question 185493This question is from textbook College Algebra A Graphing Approach
: #46
Solve for x
3/x+1=3/x-1
I just can't seem to get this one to work out.
I think the answer is x^2-x-3=0
Thanks for your help. This question is from textbook College Algebra A Graphing Approach

Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation 3%2Fx%2B1=3%2F%28x-1%29 ??? (parenthesis are critical in this case)


If so, then....


3%2Fx%2B1=3%2F%28x-1%29 Start with the given equation.


Take note that the LCD is x%28x-1%29


Multiply EVERY term by the LCD to clear out the fractions.



x-1%2Bx%28x-1%29=3x Simplify


x-1%2Bx%5E2-x=3x Distribute


x-1%2Bx%5E2-x-3x=0 Subtract 3x from both sides.


x%5E2-3x-1=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-3, and c=-1


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-3, and c=-1


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--4+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-1%29 to get -4


x+=+%283+%2B-+sqrt%28+9%2B4+%29%29%2F%282%281%29%29 Rewrite sqrt%289--4%29 as sqrt%289%2B4%29


x+=+%283+%2B-+sqrt%28+13+%29%29%2F%282%281%29%29 Add 9 to 4 to get 13


x+=+%283+%2B-+sqrt%28+13+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283%2Bsqrt%2813%29%29%2F%282%29 or x+=+%283-sqrt%2813%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%283%2Bsqrt%2813%29%29%2F%282%29 or x+=+%283-sqrt%2813%29%29%2F%282%29


which approximate to x=3.303 or x=-0.303



Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28x%2B1%29=3%2F%28x-1%29
3%28x-1%29+=+3%28x%2B1%29
3x-3+=+3x+%2B+3
-3+=+3 which can't happen. So there is no value of x where this set of equations is true.
If the problem truly is
3%2Fx%2B1=3%2Fx-1 then
3+%2B+x+=+3+-+x
-x+=+x
so x = 0 is a possible answer. However 3/0 is undefined, so x=0 is not a real answer. again, no solution