Answer
Verified
411k+ views
Hint:
Here, we will elaborate the method of simplifying the algebraic fractions. A fraction is defined as the representation of the whole in equal parts. An algebraic fraction is defined as the representation of algebraic expression in the numerator and in the denominator.
Complete step by step solution:
We know that the fraction is represented in the form of \[\dfrac{p}{q}\] where the upper part of the fraction is called the Numerator and the lower part of the fraction is called the Denominator.
We know that the algebraic fraction is divided with the same number on the numerator and the denominator, so that the process is called cancelling down, so that the process of cancelling down is used to simplify the algebraic fractions.
If we are given with the same variables on the numerator and the denominator of algebraic fractions, then the variable with the least power, gets cancelled completely and then the variable with the highest power has to be changed by subtracting the exponent of the least power from the highest power. The variable with the least power can be either in the numerator or in the denominator or in both. But it is important that the variables cancelling down are the same to simplify the algebraic fractions.
Therefore, simplifying algebraic fractions is the simplest form where the fractions cannot be cancelled down further.
Note:
We know that an algebraic expression is an expression with the combination of variables, constants and operators. Algebraic fractions can be added, subtracted, multiplied or divided. Whenever algebraic fractions are added or subtracted, then the denominator has to be the same by taking the LCM of the different denominators. However, the denominator can be multiplied or divided even if the denominators of the algebraic fractions are different. Also, these four basic arithmetic operations are used to simplify the algebraic fractions.
Here, we will elaborate the method of simplifying the algebraic fractions. A fraction is defined as the representation of the whole in equal parts. An algebraic fraction is defined as the representation of algebraic expression in the numerator and in the denominator.
Complete step by step solution:
We know that the fraction is represented in the form of \[\dfrac{p}{q}\] where the upper part of the fraction is called the Numerator and the lower part of the fraction is called the Denominator.
We know that the algebraic fraction is divided with the same number on the numerator and the denominator, so that the process is called cancelling down, so that the process of cancelling down is used to simplify the algebraic fractions.
If we are given with the same variables on the numerator and the denominator of algebraic fractions, then the variable with the least power, gets cancelled completely and then the variable with the highest power has to be changed by subtracting the exponent of the least power from the highest power. The variable with the least power can be either in the numerator or in the denominator or in both. But it is important that the variables cancelling down are the same to simplify the algebraic fractions.
Therefore, simplifying algebraic fractions is the simplest form where the fractions cannot be cancelled down further.
Note:
We know that an algebraic expression is an expression with the combination of variables, constants and operators. Algebraic fractions can be added, subtracted, multiplied or divided. Whenever algebraic fractions are added or subtracted, then the denominator has to be the same by taking the LCM of the different denominators. However, the denominator can be multiplied or divided even if the denominators of the algebraic fractions are different. Also, these four basic arithmetic operations are used to simplify the algebraic fractions.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE