SOLUTION: (1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1) Algebra problem I am trying to help my daughter with, but I can't make it work out. Please help so I can explain, thanks.

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: (1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1) Algebra problem I am trying to help my daughter with, but I can't make it work out. Please help so I can explain, thanks.      Log On


   

Question 442439: (1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1)

Algebra problem I am trying to help my daughter with, but I can't make it work out. Please help so I can explain, thanks.
Found 3 solutions by stanbon, rwm, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1)
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Multiply thru by 2(x^2-1) to get:
2(x+1) + x^2-1 = 2*2
-----
2x+2+x^2-1 = 4
x^2 + 2x + 1 = 4
---
x^2 + 2x -3 = 0
Factor:
(x+3)(x-1) = 0
x = -3 or x = 1
---
But x cannot be 1 as that would make 2 of
the original fractions undefined.
---
So the only solution is x = -3
---
Checking
(1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1)
---
1/(-3-1) + 1/2 = 2/(9-1)
---
-1/4 + 1/2 = 1/4
1/4 = 1/4
====================
Cheers,
Stan H.

Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
OK
(1)/ (x-1) + (1)/ (2) = (2) / (x^2 -1)
x=-3
check
1/-4+1/2=2/8
1/4=1/4
ok
1/(x-1) + 1/2 = 2/(x^2 -1)
1/(x-1) + 1/2 = 2/(x-1)*(x+1)


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F%28x-1%29+%2B+1%2F2+=+2%2F%28x%5E2+-1%29+
First factor +x%5E2+-+1+
+1%2F%28x-1%29+%2B+1%2F2+=+2+%2F+%28%28x+-1%29%2A%28x%2B1%29%29+
Multiply both sides by +2%2A%28x-1%29%2A%28x%2B1%29+
+2%2A%28x%2B1%29+%2B+%28x-1%29%2A%28x%2B1%29+=+4+
Now multiply everything out
+2x+%2B+2+%2B+x%5E2+-+1+=+4+
+x%5E2+%2B+2x++=+3+
Solve by completing the square
+x%5E2+%2B+2x+%2B+%282%2F2%29%5E2+=+3+%2B+%282%2F2%29%5E2+
+x%5E2+%2B+2x+%2B+1+=+3+%2B+1+
Both sides are now a perfect square
+%28+x+%2B+1+%29%5E2+=+2%5E2+
Take the square root of both sides
x+%2B1+=+2+
+x+=+1+ 1st answer
and, also the negative square root,
+x+%2B+1+=+-2+
x+=+-3+ 2nd answer
----------------------
check answers:
+x+=+1+
+1%2F%28x-1%29+%2B+1%2F2+=+2%2F%28x%5E2+-1%29+
+1%2F%281-1%29+%2B+1%2F2+=+2%2F%281%5E2+-1%29+
+x+=+1+ is not allowed because +1%2F%281-1%29+=+1%2F0+
and +2%2F%281%5E2+-1%29+=+2%2F0+
and division by 0 is not allowed
-----------
x+=+-3
+1%2F%28-3-1%29+%2B+1%2F2+=+2%2F%28%28-3%29%5E2+-1%29+
+-1%2F4+%2B+1%2F2++=+2%2F8+
+-1%2F4+%2B+2%2F4+=+1%2F4+
+1%2F4+=+1%2F4+
OK
The answer is +x+=+-3+