Question

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

Answer 1

Answer:

2÷x+1÷x-3=3÷x-3

1÷x+2÷x-3÷x=-3+3

0÷x=0

0=0

hence proved

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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf{ \frac{1}{x - 1} + \frac{2}{x - 2} = \frac{3}{x - 3} } \\ \\ \sf{ \implies \:\frac{(x - 2) + (x - 1)}{(x - 1)(x - 2)} = \frac{3}{x - 3} } \\ \\ \sf{ \implies \: \frac{x - 2 + x - 1}{x {}^{2} - 3x + 2 } = \frac{3}{x - 3} } \\ \\ \sf{ \implies \:\frac{2x - 3}{x {}^{2} - 3x + 2} = \frac{3}{ x - 3 } } \\ \\ \sf{ \implies \: 3(x {}^{2} -3 x + 2) =(2x - 3)(x - 3) } \\ \\ \sf{ \implies \: 3x {}^{2} - 9x + 6 = 2x(x - 3) - 3(x - 3) } \\ \\ \sf{ \implies \:3x {}^{2} - 3x + 6 = 2x {}^{2} - 6x - 3x + 9} \\ \\ \sf{ \implies \:3x {}^{2} - 9x + 6 = 2x {}^{2} - 9x + 9} \\ \\ \sf{ \implies \:3x {}^{2} - 9x + 6 - 2x {}^{2} + 9x - 9 = 0} \\ \\ \sf{ \implies \:x {}^{2} - 3 = 0 } \\ \\ \sf{ \implies \:x {}^{2} = 3 } \\ \\ \sf{ \therefore \: \: x = \pm \sqrt{3} }$