x-2/2x+1=x+1/x?

Question

show working please

Answer 1

Multiply both sides by the common denominators:
x(2x+1)(x-2/2x+1)=x(2x+1)(x+1/x)
x(x-2)=(2x+1)(x+1)

Distributive property:
x^2-2x=2x^2+3x+1

Set it to zero:
0=x^2+5x+1

Use the quadratic formula:
x=-b±√b^2-4ac/2a
a-1, b=5, c=1

-(5)±√5^2-4(1*1)/2(1)
(-5±√25-4(1))/2
(-5±√25-4)/2
(-5±√21)/2
x=(-5+√21)/2 or (-5-√21)/2

I hope that was helpful!

Answer 2

x-2/2x+1 = x+1/x [ I assume you mean either (x-2)/2x or
(x-2)/(2x+1)]. I also assume you mean (x+1)/x.
So (x-2)/(2x+1)= (x+1)/x. We can now cross multiply to get:
(x-2) x =(2x+1)(x+1)
x^2-2x=2x^2 +3x +1
0 =x^2 +5x + 1
x = [-5 + or - sqrt 5^2 -4*1*1]/2
x= [ -5 + sqrt 21]/2 and also'
x = [-5 - sqrt 21]/2

Sorry if I have misinterpreted your equation, but you must be exact. You can't leave the interpretation in a form that can be interpreted in more than one way.

Answer 3

Subtract X from each side so
-2/2X + 1 = 1/X
Reduce -2/2X so you get
-1/X + 1 = 1/X
Muliply every term by X to get rid of the fractions so you get
-1 + X = 1
Put 1 on a single side by adding 1 to both sides so you get
X = 2
And that's your answer.

Answer 4

Brackets and spaces are your friends... Without them it's hard to know if you mean x - 2/x + 1, or (x-2)/(2x+1).