Question 993433: Please help me solve this. I have been struggling for hours!
1/x+1/(x-1)=2/(x^2-2x) Found 2 solutions by addingup, MathTherapy:Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! You don't say by what method, it can be solved completing the squares or using the quadratic formula. Here is completing the squares:
Solve for x:
1/x+1/(x-1)=2/(x^2-2x) Rewrite for convenience: 1/(x-1)+1/x= 2/(x^2-2x)
Look for a polynomial to multiply both sides in order to get rid of fractions,
multiply by (x-1) (x^2-2x):
(x-2)(x-1)-2x+x^2 = 2(x-1)
Expand out terms of the left hand side:
2x^2-5x+2= 2(x-1)
Expand out the right hand side:
2 x^2-5 x+2 = 2 x-2
Subtract 2x-2 from both sides:
2x^2-7x+4 = 0
Divide both sides by 2 to simplify:
x^2-(7 x)/2+2= 0
Solve the quadratic equation by completing the square.
Subtract 2 from both sides:
x^2-(7x)/2 = -2
Take one half of the coefficient of x and square it, then add it to both sides.
Add 49/16 to both sides:
x^2-(7x)/2+49/16= 17/16
Factor the left hand side.
(x-7/4)^2 = 17/16
Now eliminate the exponent on the left hand side by taking th sq rt both sides:
x-7/4= sqrt(17)/4 or x-7/4= -sqrt(17)/4
Now solve each equation separately:
x-7/4= sqrt(17)/4
Add 7/4 to both sides:
x = 7/4+√(17)/4 or x-7/4 = -√(17)/4
Look at the second equation: Solve for x.
Add 7/4 to both sides:
x= 7/4+√(17)/4 or x= 7/4-√(17)/4
, with: ------- Factoring out right-side denominator
(x - 1)(x - 2) + x(x - 2) = 2(x - 1) ------- Multiplying by LCD, x(x - 1)(x - 2)
As this trinomial CANNOT be factored, use the quadratic equation formula, or "completing the square" method to solve for x
You should get:
It would've been nice if you'd shown your "struggles!"
