Respuesta :

gmany

[tex]\dfrac{\frac{3}{x-1}-4}{2-\frac{2}{x-1}}=\left(\dfrac{3}{x-1}-\dfrac{4(x-1)}{x-1}\right):\left(\dfrac{2(x-1)}{x-1}-\dfrac{2}{x-1}\right)\\\\=\dfrac{3-4x+4}{x-1}\cdot\dfrac{2x-2-2}{x-1}=\dfrac{-4x+7}{x-1}\cdot\dfrac{x-1}{2x-4}\\\\=\dfrac{-4x+7}{1}\cdot\dfrac{1}{2(x-2)}=\dfrac{-4x+7}{2(x-2)}[/tex]

VirαtKσhli

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct .

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