Operations with Rational Expressions
In abstract algebra, the concept of a polynomial is extended to include formal expressions in which the coefficients of the polynomial can be taken from any field. In this setting given a field F and some indeterminate X, a rational expression is any element of the field of fractions of the polynomial ring F[X].
Source: Wikipedia
More about operations with rational expressions:
Rational number:
Rational number is the quotient of two integers. Therefore, a rational number is a number that can be written in the form x/y, where x and y are integers, and y is not zero. A rational number written in this way is commonly called a fraction.
`u/v`
Where
u `rArr` an integer
v `rArr` a nonzero integer
`5/7`,`-6/13` `rArr` Rational numbers
An integer can be writing down as the quotient of the integer and 1, every integer is a rational number.
Example problem for operations with rational expressions:
A rational number written as a fraction can be written in decimal notation.
Example:
Write 20/5 as a decimal.
Solution:
4 `rArr` This is called a terminating decimal.
5 | 20
20
0`rArr` The remainder is Zero.
`20/5`= 4
Adding operations with rational expressions with same denominators:
Example:
`5/3`+`4/3`= ?
Solution:
`5/3`+`4/3`= `5/3`+`4/3`
= `(5+4)/3`
= `(9/3)`
=`3`
I am planning to write more post on Simplifying Rational Exponents and neet pg syllabus. Keep checking my blog.
Adding operations with rational expressions with different denominator:
Just as we add fractions, rational numbers with different denominators can also be extra. By finding out the LCM, we can take the denominators to the same number.
Example:
`8/12`+`2/3`
Solution:
=`8/12`+`2/3`
12 is the LCM of 6 and 3.
=`8/12`+`8/12`
= `(8+8)/12`
= `16/12`
= `4/3`
Subtraction operations with rational expressions with same denominators:
Just as we subtract fractions, we can subtract rational numbers with same denominator.
Example:
`9/4`-`3/4`= ?
Solution:
= `9/4`-`3/4`
= `(9-3)/4`
=`6/4`
=`3/2`
Subtraction operations with rational expressions with different denominators:
Just as we subtract fractions, rational numbers also can be taken off with different denominators. The common denominator is achieved by finding out the LCM.
Example:
`-5/3`+`15/6`
Solution:
=`-5/3`+`15 /6`
=`-10/3`+`15/6`
= `(-10+15)/6`
=`5/6`
Multiplication operations with rational expressions with same denominators:
Just alike the multiplication of whole numbers and integers, multiplication of rational number are also repeated addition.
Example:
`4/5*10/2`
Solution:
=`4/5`*`10/2`
=`(4*10)/(5*2)`
=`40/10`
=`4/1`
=`4`
Multiplication operations with rational expressions with different denominators:
Example:
`6/4`*`2/10`
Solution:
=`6/4`*`2/10`
=`(6*2)/(4*10)`
=`12/40` (both terms divided by 2)
=`6/20` (both terms divided by 2)
=`3/10`
Practices problem for ration numbers:
Problem 1:
`5/3`+`1/2`= ?
Answer: `3`
Problem 2:
`2/2`+`1/2`=?
Answer: `3/2`
Problem 3:
`6/5`-`3/5`
Answer: `3/5`
Problem 4:
`2/3`-(`6/6`)
Answer:`-1/3`
Problem 5:
`5/2` *`3/2`
Answer:`15/4`
Problem 6:
`2/4`*`4/5`
Answer:`2/5`