Question

6/x-2/(x-1)=1/(x-2)​

Answer 1

Answer:

x = 4/3

x = 3

Step-by-step explanation:

Answer attached above...

pls mark me as the brainlist ....❤️

also pls follow me...

Answer 2

AnswEr:

$\Large\star\:\sf\frac{6}{x} - \frac{2}{x -1} = \frac{1}{x - 2}$

$\bullet\:\sf\ We \: can \: write \: this \: as :$

$\Large\star\:\sf\frac{1}{x - 2} - \frac{2}{x -1} = \frac{6}{x}$

$\underline{\dag\:\textsf{Let's \: head \: to \: question \: now:}}$

$\normalsize\ : \implies\sf\frac{(x - 1) + 2(x - 2)}{(x - 2)(x - 1)} = \frac{6}{x} \\ \\ \normalsize\ : \implies\sf\frac{ x - 1 + 2x - 4}{(x^2 - x - 2x + 2)} = \frac{6}{x} \\ \\ \normalsize\ : \implies\sf\frac{3x - 5}{x^2 - 3x + 2} = \frac{6}{x}$

$\scriptsize\sf\ \:\: \: \: \: [\therefore\ \red{Using \: cross \: multiplication}]$

$\normalsize\ : \implies\sf\ x(3x - 5) = 6[x^2 - 3x + 2] \\ \\ \normalsize\ : \implies\sf\ 3x^2 - 5x = 6x^2 - 18x + 12 \\ \\ \normalsize\ : \implies\sf\ 6x^2 - 18x + 12 - 3x^2 + 5x = 0 \\ \\ \normalsize\ : \implies\sf\ 3x^2 - 13x + 12 = 0$

$\scriptsize\sf{ \: \: \: \: \: \: \: \: \:[\therefore\ \red{Using \: middle \: term \: factorization}]}$

$\normalsize\ : \implies\sf\ 3x^2 - 9x - 4x + 12 = 0 \\ \\ \normalsize\ : \implies\sf\ 3x(x - 3) - 4(x - 3) \\ \\ \normalsize\ : \implies\sf\underbrace{(x - 3)}_{case 1} \underbrace{(3x - 4)}_{case 2}$

$\rule{100}2$

$\star\:\normalsize\rm\ Case \: 1:$

$\normalsize\ : \implies\sf\ (x - 3) = 0 \\ \\ \normalsize\ : \implies\sf\ x = 0 + 3 \\ \\ \normalsize\ : \implies\sf\ x = 3$

$\normalsize\ : \implies{\boxed{\sf \green{x = 1}}}$

$\star\:\normalsize\rm\ Case \: 2:$

$\normalsize\ : \implies\sf\ (3x - 4) = 0 \\ \\ \normalsize\ : \implies\sf\ 3x = 4 \\ \\ \normalsize\ : \implies\sf\ x = \frac{4}{3}$

$\normalsize\ : \implies{\boxed{\sf \green{x = \frac{4}{3}}}}$