Question

$\frac{1}{x - 1} - \frac{2}{x - 2} = \frac{3}{x - 3} - \frac{4}{x - 4}$
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Answer 1

Step-by-step explanation:

Given:-

[1/(x-1)-2/(x-2)] = [3/(x-3)-4/(x-4)]

To find:-

Solve the given equation

[1/(x-1)-2/(x-2)] = [3/(x-3)-4/(x-4)]

Solution:-

Given that :-

[1/(x-1)-2/(x-2)] = [3/(x-3)-4/(x-4)]

LCM of 1 and 2 = 2

LCM of 3 and 4 = 12

[(x-2)-2(x-1)]/[(x-1)(x-2)] = [3(x-4)-4(x-3)]/[(x-3)(x-4)]

[(x-2-2x+2)/(x^2-x-2x+2)]=[3x-12-4x+12]/[x^2-3x-4x+12]

=> -x/(x^2-3x+2) = -x/(x^2-7x+12)

On cancelling '- x 'both sides then

=> 1/(x^2-3x+2) = 1/(x^2-7x+12)

On applying cross multiplication then

=> x^2-7x+12 = x^2-3x+2

=>x^2-7x+12-x^2+3x-2 = 0

=> -4x+10 = 0

=> 4x = 10

=>x = 10/4

=> x = 5/2

Answer:-

The value of x for the given problem is 5/2

Answer 2

hope it will help you.

good night.