Which expression is equivalent to the following complex fraction?
3/x-1 -4/ 2-2/x-1
To simplify the expression, we first need to find a common denominator for the two fractions within the complex fraction. The common denominator for the fraction "3/(x-1)" and "4/(2 - 2/(x-1))" is "(x-1)".
Now, we can rewrite the complex fraction using the common denominator:
3/(x-1) - 4/(2 - 2/(x-1)) = (3(x-1))/(x-1) - (4(x-1))/(2(x-1) - 2/(x-1))
Next, we can simplify further:
= 3 - (4(x-1))/(2x-2 - 2/(x-1))
= 3 - (4(x-1))/(2x-2 - 2/(x-1))
= 3 - (4(x-1))/(2x-2 - (2(x-1))/(x-1))
= 3 - (4(x-1))/(2x-2 - (2x-2)/(x-1))
= 3 - (4(x-1))/(2x-2 - 2x + 2)/(x-1))
= 3 - (4(x-1))/(-2x)/(x-1))
= 3 - (4(x-1))/(-2x)
Now, we can simplify the negative sign:
= 3 + (4(x-1))/(2x)
= 3 + 2(x-1)/x
Therefore, the expression that is equivalent to the given complex fraction is "3 + 2(x-1)/x".