Question

Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`

Answer 1

`3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3, `

This can be rewritten as:

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

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

`(7x-5)/(3x^2+2x-1)=1/2`

On cross multiplying, we get:

2(7x-5)=3x²+2x-1

14x-10=3x²+2x-1

3x²-12x+9=0

3x²-9x-3x+9=0

3x(x-3)-3(x-3)=0

(3x-3)(x-3)=0

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

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

x=1,3

Thus, the solution of the given equation is 1 or 3.