Complex fraction
Simplify complex fractions with fractions in numerator or denominator: multiply by the LCD of all inner fractions to clear nested structure and produce a simple rational expression.
Key Concepts
A complex fraction is a fraction that contains one or more fractions in its numerator or denominator.
$$\frac{\frac{x}{3}}{x+1}$$ $$\frac{2+\frac{1}{a}}{2b+5}$$ $$\frac{y+\frac{3}{y}}{y \frac{1}{4y}}$$.
Imagine a fraction throwing a party, and its guests are other fractions! That's a complex fraction—a fraction inside another fraction. It looks like a multi level puzzle, but don't worry. Our goal is to flatten this 'fraction ception' into a single, simple fraction. It’s really just a fancy division problem waiting to be solved and simplified.
Common Questions
What is a complex fraction?
A complex fraction is a fraction where the numerator, the denominator, or both contain fractions. For example, (1/x)/(1/x + 1) is a complex fraction. Simplifying it requires clearing the nested fractions to produce a single rational expression.
What is the best method to simplify a complex fraction?
Find the LCD of all the smaller fractions within the complex fraction. Multiply every term in the numerator and denominator by this LCD. This eliminates all inner fractions simultaneously, leaving a polynomial numerator and denominator that can be simplified by factoring and canceling.
Can you simplify a complex fraction by dividing numerator by denominator?
Yes. Simplify the numerator into one fraction and the denominator into one fraction separately, then divide by multiplying by the reciprocal. Both methods give the same result; the LCD method is often faster for complex algebraic expressions.