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## Simplifying Complex Fractions: Which Expression Is Equivalent To The Following Complex Fraction 3/x-1-4/2-2/x-1

Complex fractions are fractions that have fractions within them. To simplify a complex fraction, we need to combine the fractions into a single fraction with a common denominator. Let’s simplify the following complex fraction:

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

### Steps to Simplify:, Which expression is equivalent to the following complex fraction 3/x-1-4/2-2/x-1

- Find the least common multiple (LCM) of the denominators (x-1) and (2-x). The LCM is (x-1)(2-x).
- Multiply the numerator and denominator of each fraction by the missing factor from the LCM.
- Combine the fractions with the common denominator.
- Simplify the numerator by combining like terms.

### Solution:

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

(2-x)/(2-x) = 6/(x-1)(2-x)

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

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

- 6/(x-1)(2-x)
- 4(x-1)/(x-1)(2-x)
- 4(2-x)/(x-1)(2-x) = (-4x + 10)/(x-1)(2-x)

Therefore, the simplified complex fraction is (-4x + 10)/(x-1)(2-x).

## FAQ Section

**What is the first step in simplifying the given complex fraction?**

The first step is to find a common denominator for the three fractions.

**What is the domain of the simplified complex fraction?**

The domain is all real numbers except for x = 1 and x = 2.

Continue this structure for all FAQs