# Complex Rational Expressions

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Complex rational expression is a useful tool. It helps to convert a complex rational expression into simplified
expression. An expression in which both numerator and denominator or either one contains a rational expression is known as a complex rational expressions. The complex rational expressions may contain algebraic fractional expression or just a fraction. There are 2 methods to solve complex fractions. One is finding common denominator for each expression and simplifying. The 2nd method is to find common fraction that we multiply with all the terms to simplify. This tool complex rational expression is also an online calculator that intakes complex rational expressions and converts them into simple expression.

Example 1: Simplify by complex fraction solver

2 + 2/x

-------------------------

4 – 3/x^2

Solution: We will simplify numerator 1st; 2 + 2/x = (2x+2)/ x

(Now simplify denominator) 4 - (3/ x^2) = (4x^2 - 3) / x^2

Now inverse the denominator fraction and multiply numerator and denominator we get, (2(x + 1) /x ) (x^2 /

(4x^2 - 3))

2(x+1 ) x

= -------------- = (2x^2+2x) / (4x^2-3)

4x^2 - 3

Example 2: Simplify by complex fraction solver

3/q-1 + 1/q-2 divide by 5/q-2 + 2/q-1

Solution: Simplify numerator we get

3/(q-1) + 1/(q-2) = [(3q-6)+(q-1)]/(q-1)(q-2)

Simplify denominator we get

5/q-2 + 2/q-1 = [5(q-1)+2(q-2)]/(q-2) (q-1)

When we reverse the denominator fraction we can multiply it with numerator

[(3q-6) + (q-1)]  x (q-2) (q-1)                   3(q-2)+(q-1)              4q-7

------------------------------------------------ =  ------------------------- =  --------------

(q-1)(q-2)         x    [5(q-1)+2(q-2)]        5(q-1)+2(q-2)              7q-9