Question

Giải phương trình :

a,2x+1/2x-1 - 2x-1/2x+1=8/4x^2-1

b,x+1/x-1 - x-1/x+1=3x.{1- x-1/x+1}

Answer 1

a)⇔(2x+1)(2x+1)/(2x-1)(2x+1)-(2x-1)(2x-1)/(2x-1)(2x+1)=8/(2x-1)(2x+1)

⇔(2x+1)^2-(2x-1)^2=8

⇔[(2x+1)-(2x-1)][(2x+1)(2x-1)]=8

⇔2.4x=8

⇔x=1.S={1}

Answer 2

a: \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{4x^2-1}\)

=>(2x+1)^2-(2x-1)^2=8

=>4x^2+4x+1-4x^2+4x-1=8

=>8x=8

=>x=1

b: \(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=3x\cdot\left(1-\dfrac{x-1}{x+1}\right)\)

=>\(\dfrac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}=3x\cdot\dfrac{x+1-x+1}{x+1}\)

=>\(\dfrac{4x}{\left(x-1\right)\left(x+1\right)}=3x\cdot\dfrac{2}{x+1}\)

=>4x=6x(x-1)

=>6x^2-6x-4x=0

=>6x^2-10x=0

=>2x(3x-5)=0

=>x=0 hoặc x=5/3