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Which expression is equivalent to the following complex fraction?


StartFraction 3 Over x minus 1 EndFraction minus 4 divided by 2 minus StartFraction 2 Over x minus 1 EndFraction

Which expression is equivalent to the following complex fraction StartFraction 3 Over x minus 1 EndFraction minus 4 divided by 2 minus StartFraction 2 Over

Answer :

The equivalent expression for the given complex fraction is [tex]\frac{-4x + 7}{2(x - 2)}[/tex].

The given parameters;

  • complex fraction = [tex]\frac{\frac{3}{x - 1}- 4 }{2 - \frac{2}{x - 1} }[/tex]

The numerator is simplified as follows;

  • [tex]\frac{3}{x- 1} - 4 = \frac{3 - 4(x-1)}{x-1} = \frac{3 - 4x + 4}{x-1} = \frac{7 - 4x}{x-1}[/tex]

The denominator is simplified as follows;

  • [tex]2 - \frac{2}{x - 1} = \frac{2(x-1) - 2}{x- 1} = \frac{2x - 2 - 2}{x-1} = \frac{2x - 4}{x-1}[/tex]

The expression can be simplified further by dividing the numerator by the denominator as follows;

  • [tex]\frac{7 - 4x}{x - 1} \times \frac{x - 1}{2x - 4} = \frac{7 - 4x}{2x - 4} = \frac{7- 4x}{2(x - 2)} = \frac{-4x + 7}{2(x - 2)}[/tex]

Thus, the equivalent expression for the given complex fraction is [tex]\frac{-4x + 7}{2(x - 2)}[/tex].

Learn more about simplification of fractions here: https://brainly.com/question/78672

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Rewritten by : Barada

Answer: the second option is the correct answer

Step-by-step explanation:

The given expression is

[3/(x - 1) - 4]/[2 - 2/(x - 1)

We would simplify the numerator first. The LCM of the numerator is

x - 1. Taking the LCM of the numerator, it becomes

[3 - 4(x - 1)]/(x - 1)

= [3 - 4x + 4]/(x - 1)

= (- 4x + 7)/(x - 1)

We would simplify the denominator. The LCM of the denominator is

x - 1. Taking the LCM of the numerator, it becomes

[2(x - 1) - 2]/(x - 1)

= [2x - 2 - 2]/(x - 1)

= (2x - 4)/(x - 1)

= 2(x - 2)/(x - 1)

The expression becomes

[(- 4x + 7)/(x - 1)]/[ 2(x - 2)/(x - 1)]

= (- 4x + 7)/(x - 1) × (x - 1)/2(x - 2)

(x - 1) cancels out. It becomes

(- 4x + 7) / 2(x - 2)