SOLUTION: Hi, I don't get how this equation works. I have the answer, but I don't know why it's the answer: 1/(x^2 + 1) + 1/(x+1) = x/(x^2-1) Could you please have a step-by-step explanati

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Hi, I don't get how this equation works. I have the answer, but I don't know why it's the answer: 1/(x^2 + 1) + 1/(x+1) = x/(x^2-1) Could you please have a step-by-step explanati      Log On


   

Question 1017812: Hi, I don't get how this equation works. I have the answer, but I don't know why it's the answer:
1/(x^2 + 1) + 1/(x+1) = x/(x^2-1)
Could you please have a step-by-step explanation? Thanks in advance!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%5E2+%2B+1%29+%2B+1%2F%28x%2B1%29+=+x%2F%28x%5E2-1%29
Simplest common denominator is %28x%5E2%2B1%29%28x-1%29%28x%2B1%29.

Multiply left and right members by the common denominator.

%28x-1%29%28x%2B1%29%2B%28x%5E2%2B1%29%28x-1%29=x%28x%5E2%2B1%29
x%5E2-1%2Bx%5E3-x%5E2%2Bx-1=x%5E3%2Bx
x%5E3%2Bx%5E2-x%5E2-2=x%5E3%2Bx
-x%5E2-2=x
x%5E2%2B2=-x
x%5E2%2B2%2Bx=0
x%5E2%2Bx%2B2=0-------not factorable with integer coefficients.

x=%28-1%2B-+sqrt%281-4%2A2%29%29%2F2

x=%28-1%2B-+sqrt%28-7%29%29%2F2

highlight%28x=%28-1%2B-+i%2Asqrt%287%29%29%2F2%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, I don't get how this equation works. I have the answer, but I don't know why it's the answer:
1/(x^2 + 1) + 1/(x+1) = x/(x^2-1)
Could you please have a step-by-step explanation? Thanks in advance!
The equation, after multiplying by the LCD, becomes: 0 on one side and 2 on the other. 

Because 0+%3C%3E+2, highlight_green%28matrix%281%2C2%2CNO%2C+SOLUTION%29%29 exists.