Question

Please say the solution in book ​

Answer 1

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

∴3/x-2/x-3=1/x-3

∴3-2/x-3=1/x-3

=0

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Answer 2

Explanation :

$\longrightarrow \rm \: \dfrac{3}{x - 1} - \dfrac{2}{x - 2} = \dfrac{1}{x - 3} \\ \\ \\ \longrightarrow \rm \: \dfrac{3}{x - 1} - \dfrac{2}{x - 2} - \dfrac{1}{x - 3} = 0 \\ \\ \\ \longrightarrow \rm \: \dfrac{3(x - 2) \times (x - 3) - 2(x - 1) \times (x - 3) - 1(x - 1)(x - 2) }{(x - 1) \times (x - 2) \times (x - 3)} = 0 \\ \\ \\ \longrightarrow \rm \: \dfrac{(3x - 6) \times (x - 3) + ( - 2x + 1) \times (x - 3) - (x {}^{2} - 2x - x + 2) }{(x - 1) \times (x - 2) \times (x - 3)} = 0 \\ \\ \\ \longrightarrow \rm \: \dfrac{3x {}^{2} - 9x - 6x + 18 - 2x {}^{2} + 6x + 2x - 6 - (x {}^{2} - 3x + 2 ) }{(x - 1) \times (x - 2) \times (x - 3)} = 0 \\ \\ \\ \longrightarrow \rm \: \dfrac{3x {}^{2} - 9x - 6x + 18 - 2x {}^{2} + 6x + 2x - 6 - x {}^{2} + 3x - 2 }{(x - 1) \times (x - 2) \times (x - 3)} = 0 \\ \\ \\ \longrightarrow \rm \dfrac{0 - 4x + 10}{(x - 1) \times (x - 2) \times (x - 3)} = 0 \\ \\ \\ \longrightarrow \rm - 4x + 10 = 0 \times (x - 1) \times ( x- 2) \times x - 3) \\ \\ \\ \longrightarrow \rm - 4x + 10 = 0 \\ \\ \\ \longrightarrow \rm - 4x = - 10 \\ \\ \\ \longrightarrow \rm x = \dfrac{ \not{ - }10}{ \not{ -} 4} \\ \\ \\ \longrightarrow \red{\rm x = \dfrac{5}{2} }$