Question

1/x+1/2x-3=1/2 solve​

Answer 1

Step-by-step explanation:

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}

x

1

+

2x−3

2

=

x−2

1

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}

x(2x−3)

2x−3+2x

=

x−2

1

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

2x

2

−3x

4x−3

=

x−2

1

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

2

−3x)(x−2)

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

2

−3x)

simplify the above expression,

4x^{2}-3x-8x+6=2x^{2}-3x4x

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

4x^{2}-8x+6-2x^{2}=04x

2

−8x+6−2x

2

=0

2x^{2}-8x+6=02x

2

−8x+6=0

divide both the sides by 2 in above

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

2

−4x+3=0

factoring the above expression,

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

2

−x−3x+3=0

x(x-1)-3(x-1)=0x(x−1)−3(x−1)=0

(x-1)(x-3)=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