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Complex Fractions

The common fractions is the fractions in which the numerator or denominator or both contain fractions. Note: In first example, its numerator is a fraction. In second fraction, its denominator is a fraction. In the third example, both numerator and denominator are fraction.

Example

Simplify Complex Fraction To Simple Fraction (Method 1)

The denominator of the simple fraction is the product of inner items of the given complex fraction and the numerator of the simple fraction is the product of the outer items of the given complex fraction.

Example

Simplify Complex Fraction To Simple Fraction (Method 2)

Express the complex fraction as a quotient of simple fractions, change division to multiplication, then simplify the result.

Example

Simplify Complex Fraction To Simple Fraction (Method3)

First find the least common denominator (LCD) of all fractions in the numerator and denominator of the complex fraction, second multiply the numerator and denominator of the complex fraction by the least common denominator (LCD), and then simplify the result.

Note: Look the example shown below, the least common denominator in numerator is x(x - 1), the least common denominator in denominator is x, so the least common denominator in this complex fraction is x(x - 1), so the first step of the solution is to multiply x(x - 1) on both numerator and denominator of the complex fraction,  the second step of the solution is that each term of the complex fraction  multiply the x(x - 1) to simplify the fraction.

Example

Application of Complex Fraction

In electronics, if resistors are connected in parallel, then the reciprocal of the total resistance equals to the sum of the reciprocals of the resistance of each component.

Example