Math, asked by debashreebanerjee78, 5 months ago

solve: 6/x-2/x-1=1/x-2​

Answers

Answered by tennetiraj86
2

Answer:

answer for the given problem is given

Attachments:
Answered by ItzNightLight
36

Answer:

 \frac{6}{x}  -  \frac{2}{x - 1}  =  \frac{1}{x - 2 } \\  \frac{6(x - 1) - 2x}{x(x - 1)}  =  \frac{1}{x - 2}  \\  \frac{6x - 6 - 2x}{ {x}^{2} - x }  =  \frac{1}{x - 2}  \\  \frac{4x - 6}{ {x}^{2} - x } =   \frac{1}{x - 2}  \\ (4x - 6)(x - 2) = ( {x}^{2}  - x) \\ 4 {x}^{2}  - 8x - 6x + 12 =  {x}^{2}  - x \\ 4 {x}^{2}  - 14x + 12  -  {x}^{2} + x = 0 \\  {x}^{2}  - 13x + 12 = 0

3 {x}^{2}  - 9x - 4x + 12 = 0 \\ (by \:  splitting  \: the  \: middle \:  term \: Theorem)

  3 {x}^{2}  - 9x - 4x + 12 = 0 \\ x( x  - 3) - 4(x - 3) = 0 \\  \\ (x - 3)(x - 4) = 0

Now, \\ x - 3 =0 \\ x = 3  \\  \\ And \\ x - 4 = 0 \\ x = 4

 \bold {value \: of \: x \: is \: 3 \: and \: 4}

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