which expression is equivalent to the following complex fraction?\n$\frac{\frac{3}{x - 1}-4}{2-\frac{2}{x…

which expression is equivalent to the following complex fraction?\n$\frac{\frac{3}{x - 1}-4}{2-\frac{2}{x - 1}}$\n$\frac{2(x - 2)}{-4x + 7}$\n$\frac{-4x + 7}{2(x - 2)}$\n$\frac{-4x + 7}{2(x^{2}-2)}$\n$\frac{2(x^{2}-2)}{-4x + 7}$

which expression is equivalent to the following complex fraction?\n$\frac{\frac{3}{x - 1}-4}{2-\frac{2}{x - 1}}$\n$\frac{2(x - 2)}{-4x + 7}$\n$\frac{-4x + 7}{2(x - 2)}$\n$\frac{-4x + 7}{2(x^{2}-2)}$\n$\frac{2(x^{2}-2)}{-4x + 7}$

Answer

Explanation:

Step1: Simplify the numerator

First, find a common - denominator for the numerator $\frac{3}{x - 1}-4$. The common denominator is $x - 1$. So, $\frac{3}{x - 1}-4=\frac{3-4(x - 1)}{x - 1}=\frac{3-4x + 4}{x - 1}=\frac{-4x+7}{x - 1}$.

Step2: Simplify the denominator

Next, find a common - denominator for the denominator $2-\frac{2}{x - 1}$. The common denominator is $x - 1$. So, $2-\frac{2}{x - 1}=\frac{2(x - 1)-2}{x - 1}=\frac{2x-2 - 2}{x - 1}=\frac{2x-4}{x - 1}=\frac{2(x - 2)}{x - 1}$.

Step3: Rewrite the complex fraction

The original complex fraction $\frac{\frac{3}{x - 1}-4}{2-\frac{2}{x - 1}}$ can be rewritten as $\frac{\frac{-4x + 7}{x - 1}}{\frac{2(x - 2)}{x - 1}}$.

Step4: Divide the fractions

When dividing by a fraction, we multiply by its reciprocal. So, $\frac{\frac{-4x + 7}{x - 1}}{\frac{2(x - 2)}{x - 1}}=\frac{-4x + 7}{x - 1}\times\frac{x - 1}{2(x - 2)}=\frac{-4x + 7}{2(x - 2)}$.

Answer:

$\frac{-4x + 7}{2(x - 2)}$