Question

solve for x: 1/x+2/2x-3=1/x-2,x≠0,3/2,2

Answer 1

The values of x are 3 and 1...

Answer 2

Answer:

The value of x are 1 and 3

Step-by-step explanation:

we need to find the value of x

The given expression is :

$\frac{1}{x}+\frac{2}{2x-3}=\frac{1}{x-2}$  where x ≠ 0 ,3/2 ,2

Take L.C.M of x and 2x-3

$\frac{2x-3+2x}{x(2x-3)}=\frac{1}{x-2}$

$\frac{4x-3}{2x^{2}-3x}=\frac{1}{x-2}$

Multiply both the sides by $(2x^{2}-3x)(x-2)$

$(4x-3)(x-2)=(2x^{2}-3x)$

simplify the above expression,

$4x^{2}-3x-8x+6=2x^{2}-3x$

Cancel the like terms in left and right hand side and simplify further

$4x^{2}-8x+6=2x^{2}$

$4x^{2}-8x+6-2x^{2}=0$

$2x^{2}-8x+6=0$

divide both the sides by 2 in above

$x^{2}-4x+3=0$

factoring the above expression,

$x^{2}-x-3x+3=0$

$x(x-1)-3(x-1)=0$

$(x-1)(x-3)=0$

if x-1 =0 ⇒  x=1

if x-3 =0 ⇒ x=3

Therefore, the value of x are 1 and 3