Which expression is equivalent to the following complex fraction?

Question 1

$Which expression is equivalent to the following complex fraction?-example-1$

Question 2

Answer:

Option B

Explanation:

Numerator:

$(3)/(x -1 )-4 =(3)/(x-1)-(4*(x-1))/(x-1)\\\\$

$=(3- 4x -4*(-1))/(x-1)=(3-4x+4)/(x-1)\\\\\\=(-4x+7)/(x-1) \: \textbf{ [Combine like terms]}$

Denominator:

$2-(2)/(x-1)=(2*(x-1))/(x-1)-(2)/(x-1)\\$

$= \bf (2x-2-2)/(x-1)\\\\\\= (2x-4)/(x-1)\\\\= (2*(x- 2))/(x-1)$

((3)/(x-1)-4)/(2-(2)/(x-1))=((-4x+7)/(x-1))/((2*(x-2))/(x-1))

$\bf = (-4x+7)/(x-1)*(x-1)/(2(x-2)) \ \ \ \textbf{ [(x-1) in the numerator and denominator will be cancelled]}\\\\\\=(-4x+7)/(2(x-2))$

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