As discussed earlier rational expressions are nothing but fractions of the form $\frac{P}{Q}$ where P and Q both are mathematical expressionsand Q is not equal to 0.
Rational expressions play a major role in Algebra and very often we will deal with them.
In this section will learn to identify rational expressions, operations on them like addition and subtraction of rational expressions etc. and simplification of rational expressions.
Solving Rational Expressions
A rational expression is an algebraic expression of the form A/B, where A and B are simpler expressions and the denominator B is not zero.
We call A the numerator B is the denominator of rational expression. A/B need not to be a polynomial. Mostly, polynomials are rational numbers as if B is a polynomial, then it can be written as 1/B.
3x?45x^2+2x+3 is a rational expression whose numerator is a linear polynomial and the denominator is a quadratic polynomial.
5x^3+2x+3x^4?3x^2?6x?4 is a rational expression whose numerator is a polynomial of a degree 4 and the denominator is a polynomial of a degree 3.
Here's an example on solving Rational expressions:
Solve `((8a)/7)/((4a)/21)` .
Solution:
Step 1: `((8a)/7)/((4a)/21)`
Step 2: The terms in the denominator is revesed and multiplied with the numberator.
`((8a)/7)` `xx` `(21/(4a))`
Step 3: The resultant fraction is reduced to the simplest form,
`(8a)/(4a)`
Step 4: Eliminate the same or like terms,
`8/4`
This is the obtained result for solving the complex rational expressions.
Rational Expressions Calculator
The students can learn how to work with the Rational Expressions Calculator. The Rational expressions calculator helps to conduct the operations like subtraction, division, multiplication and ddition on the rational expressions with ease. Here are some examples showing the operations being conducted on rational expressions:
Simplify: (x2-x-6)/(x2+5x+6)
=`((x^2-x-6))/((x^2+5x+6))`
=`((x-3)(x+2))/((x+2)(x+3))`
=`((x-3))/((x+3))`
Simplify :(x2-2x+ 1) / (x2-3x+2) * (3x-6) / (6x-6)
Solution :x2 – 2x + 1 = (x–1)2
x2– 3x + 2 = (x – 2) (x – 1);
6x – 6 = 6(x –1)
3x – 6 = 3( x – 2)
`((x-1)(x-1))/((x-1)(x-2))` * `(6(x-1))/(3(x-2))`
`2(x-1)^2/((x-2))`