Solving Complex Rational Expressions

Rational Expressions: Rational expressions are defined as one of the basis of mathematics. All the rational are having polynomials terms in both of the numerator function and the denominator function. The polynomials are present along with the variables.

 Complex rational expressions: Complex rational expressions are having the polynomials with the fraction format. The expressions should have atleast one fraction with the polynomials.
Explanations for Solving Complex Rational Expressions

There are many steps are followed for solving the complex rational expressions. They are defined as follows,

Step 1: Write the given rational expressions.

Step 2: Bring the denominator terms to the multiplication format by taking inverse.

Step 3: Then in the next step, we have to solve the obtained result.
Example Problem for Solving Complex Rational Expressions

Problem 1: Solve the given rational expressions, `((4a)/3)/((3a)/2)` .

Solution:

Step 1: Write the given complex rational expressions,

`((4a)/3)/((3a)/2)`

Step 2: Bring the denominator terms to the numerator by taking the inverse, we get,

`((4a)/3)` `xx` `(2/(3a))`

Step 3: In the next step, we have to simplify the obtained terms,we get,

`(8a)/(9a)`

Step 4: By eliminating the like terms, we get,

`8/9`

This is the obtained result for solving the complex rational expressions.

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Problem 2: Solve the given rational expressions, `((6a)/3)/((9a)/4)` .

Solution:

Step 1: Write the given complex rational expressions,

`((6a)/3)/((9a)/4)`

Step 2: Bring the denominator terms to the numerator by taking the inverse, we get,

`((6a)/3)` `xx` `(4/(9a))`

Step 3: In the next step, we have to simplify the obtained terms,we get,

`(8a)/(9a)`

Step 4: By eliminating the like terms, we get,

`8/9`

This is the obtained result for solving the complex rational expressions.

Problem 3: Solve the given rational expressions, `((8a)/2)/((4a)/2)` .

Solution:

Step 1: Write the given complex rational expressions,

`((8a)/2)/((4a)/2)`

Step 2: Bring the denominator terms to the numerator by taking the inverse, we get,

`((8a)/2)` `xx` `(2/(4a))`

Step 3: In the next step, we have to simplify the obtained terms,we get,

= 2

This is the obtained result for solving the complex rational expressions.
Practice Problem for Solving Complex Rational Expressions

Problem 1: Solve the given rational expressions, `((5a)/10)/((25a)/5)` .

Answer: `1/10`

Problem 1: Solve the given rational expressions, `((5a)/4)/((15a)/8)` .

Answer: `2/3`