3/x-1+1/x-3=4/x-2. Find x.

Given equation

3/x-1+1/x-3=4/x-2

We need to find the value of x

3/x-1+1/x-3=4/x-2

On taking LCM in LHS we get

3(x-3) + 1 (x-1) / (x-1)(x-3)= 4/ x-2

=>3x-9 + x-1 / (x-1)(x-3) = 4/ x-2

=> (4x -10) (x-2) = 4 (x-1) (x-3)

= >4×2 – 8x -10x+20= 4 (x2 -3x -x+3)

=> 4x2 -18x +20 = 4x2 – 12x -4x +12

=> 4x2 -18x +20 = 4x2 – 16x +12

4x2 gets cancelled on both sides

=> -18x +20 = – 16x +12

=> -18x+16x = 12 – 20

=> -2x = -8

Negative sign gets cancelled on both sides

=> 2x= 8

=> x= 8/2

=>x=4

Hence x=4

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