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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
