Question

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

Answer 1

Step-by-step explanation:

LHS

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

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

= x-5 / (x-2) (x-3) -----------(1)

RHS

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

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

= x+5 / (x-3) (x-1) ------------(2)

Equating (1) & (2),

x-5 / (x-2) (x-3) = x+5 / (x-1) (x-3)

{x-3 gets cancelled}

x-5 / x-2 = x+5 / x-1

(x-5) (x-1) = (x+5) (x-2)

x^2-x-5x+5 = x^2-2x+5x-10

{x^2 gets cancelled}

-6x-3x = -10-5

-9x = -15

x = 15/9

x = 5/3

Hope it helps.....

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