# Solve the Following Quadratic Equations by Factorization: 1/X-1/(X-2)=3 , X ≠ 0, 2 - Mathematics

Solve the following quadratic equations by factorization:

1/x-1/(x-2)=3 , x ≠ 0, 2

#### Solution

We have been given

1/x-1/(x-2)=3

-2 = 3x2 - 6x

3x2 - 6x + 2 = 0

3x^2 - (3 + sqrt3)x-(3-sqrt3)x+3-sqrt3+sqrt3-1=0

x(3x-3-sqrt3)+((-3+sqrt3)/3)(3x-3-sqrt3)=0

((3x-3+sqrt3)/3)(3x-3-sqrt3)=0

(sqrt3x-sqrt3+1)(sqrt3x-sqrt3-1)=0

Therefore,

sqrt3x-sqrt3+1=0

sqrt3x=sqrt3-1

x(sqrt3-1)/sqrt3

or

sqrt3x-sqrt3-1=0

sqrt3x=sqrt3+1

x(sqrt3+1)/sqrt3

Hence, x(sqrt3-1)/sqrt3 or x(sqrt3+1)/sqrt3

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths