Answer:
second option
Step-by-step explanation:
Simplify the numerator and denominator, that is
[tex]\frac{3}{x-1}[/tex] - 4
= [tex]\frac{3-4(x - 1)}{x-1}[/tex] = [tex]\frac{3-4x+4}{x-1}[/tex] = [tex]\frac{-4x+7}{x-1}[/tex]
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2 - [tex]\frac{2}{x-1}[/tex]
= [tex]\frac{2(x-1)-2}{x-1}[/tex] = [tex]\frac{2x-2-2}{x-1}[/tex] = [tex]\frac{2x-4}{x-1}[/tex] = [tex]\frac{2(x-2)}{x-1}[/tex]
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The expression can now be expressed as
[tex]\frac{-4x+7}{x-1}[/tex] ÷ [tex]\frac{2(x-2)}{x-1}[/tex]
To calculate the division, change division to multiplication and turn the second fraction upside down, that is
[tex]\frac{-4x+7}{x-1}[/tex] × [tex]\frac{x-1}{2(x-2)}[/tex] ← cancel (x - 1) on numerator/ denominator, leaving
[tex]\frac{-4x+7}{2(x-2)}[/tex]
