SOLUTION: please help me with this problem solve for x x=3/x+1 this is what i have so far x(x+1)=3 (x+3)(x-1)=0 ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me with this problem solve for x x=3/x+1 this is what i have so far x(x+1)=3 (x+3)(x-1)=0 ?      Log On


   

Question 34577: please help me with this problem
solve for x
x=3/x+1
this is what i have so far
x(x+1)=3
(x+3)(x-1)=0
?
Found 2 solutions by MrTillman, Earlsdon:
Answer by MrTillman(3) About Me  (Show Source):
You can put this solution on YOUR website!
First thing you need to do is get rid of the fraction, thus you multiply x by each term, which gives you a quadratic equation: x%28x%29=%28x%293%2Fx+%2B+1%28x%29
x%5E2=3x%2Fx+%2B+x
x%5E2=3+%2B+x set equal to 0
x%5E2-x-3=0
This quadractic doesnt factor, so you have to 'complete the square' like this: first isolate the variable terms to get x%5E2-x=3
Make sure first term has coefficient of 1, it does
Then take coefficient of middle term (-x) and find the perfect square trinomial like this: %28-1%2F2%29%5E2 which gives you 1/4 or .25
Just add this to both sides to x%5E2-x%2B1%2F4=3%2B1%2F4 and you get x%5E2-x%2B1%2F4=13%2F4
Now you can factor the left side of this to get %28x-1%2F2%29%5E2=13%2F4
Now you can solve for x using the square root method by taking square root of both sides to get x-1%2F2+=+sqrt%2813%2F4%29 = x-1%2F2=1.803 x+=+1.803%2B1%2F2
x= 2.303
Check 2.303 = 3/2.303 + 1
2.303=1.303+1 yes

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: Your first step is correct.
x+=+3%2F%28x%2B1%29 Multiply both sides by (x+1)
x%28x%2B1%29+=+3 Simplify...here's where you erred!
x%5E2+%2B+x+=+3 Subtract 3 from both sides.
x%5E2+%2B+x+-+3+=+0 Solve this quadratic equation using the quadratic formula:x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a.
x=%28%28-1%29%2B-sqrt%281%5E2-4%281%29%28-3%29%29%29%2F2%281%29
x=%28%28-1%29%2B-sqrt%2813%29%29%2F2