Rationalizing the Denominator

Previously we have discussed about area of octagon calculator and In today's session we are going to discuss about Rationalizing the Denominator which comes under andhra pradesh state education board, It defines the method to rewrite a fraction in a form containing merely rational numbers in the denominator. Finding the equivalent expression (which in the denominator not have any radicals) of a radical expression is required in algebra and is known as rationalizing the denominator. In simple words when moving a root value from the bottom of a fraction to the top of fraction is called as rationalizing the denominator . There are basically three types of cases in algebra( check out Algebra Answers for reference) that are:
( a ) square root
( b ) cube root or other roots of higher category
( c ) square root addition or difference
In case ( a ), when in the denominator there is a only single square root then the rationalization process of denominator is done only by multiplying numerator and denominator with the square root. We can understand it by an example as 1 / √ 3 is rationalized by multiplying √ 3 to both numerator and denominator of the fraction. (Know more about  in broad manner, here,)
( 1 / √ 3 ) * √ 3 / √ 3 = √ 3 / 3
In case ( b ) when there is higher root (means cube root etc) in the denominator then we multiply and divide the fraction with something that provides the perfect power. For example if there is cube root of 3 in the denominator than we can multiply it by 9 that is the 2nd power of 3 .
We can understand it also by an example as 1 / ³√ p q that is solved as
1 / ³√ p q = 1 / √ p q * ³√ p ² q ² / ³√ p ³ q ³ = ³√ p² q ²/ p q
In case ( c ) numerator and denominator are multiplied with their difference which can be sum or vice versa . To understand it, one example is discussed that is 7 / 9 + √ 10 then
= 7 / 9 + √ 10 * 9 - √ 10 / 9 - √ 10
= 7 ( 9 - √ 10 ) / 81 – 10
= 63 – 7 √ 10 / 71 .
In the next session we are going to discuss about fractional notation calculator
and if anyone want to know about Inequalities then they can refer to Internet and text books for understanding it more precisely.

Equations with no Solution

Friends, Previously we have discussed about area of an octagon calculator and today we are going to discuss about the linear equations with no solution which is a part of ap state board of secondary education. Before I start first I will tell you about what is linear equation and solving linear equations. A linear equation is an algebraic equation which consists of a term that can be a single variable and constant or product of constants. A linear equation may have more than one variable.
A linear equation can have no solution. For instance:
0x + 2 = 5; here in this given linear equation since 0 is multiplied by x so this will result in a 0. And 0 + 2 is not equals to 5, so from this we can say that any linear equation has a zero as the coefficient of x will not give any solution. Such equations are known as Equations with no Solution.
Whenever we start solving an equation, we always try to make its simplest form. We always start with an assumption that the equation is having an actual solution. We try to solve it and when we end it with an uncertain and wrong answer then it indicates that our assumption was wrong and the equation has no solution. So the statement 2 = 5 in above example is false.
Let’s take one more example: Solve the equation      12 + 5x – 9 = 7x + 5 – 3x
Solution: 12 + 5x – 9 = 7x + 5 – 3x       (given equation)
12 -9 – 5 = 7x –2 x – 5x          (simplify it)
-2 = 0  (Answer)
So the above example gave the result -2 = 0 that is not true; that means that this equation has no solution.(want to Learn more about Equations, click here),
So such equations which has 0 as a coefficient of the variable or the equations which give a wrong or false statement are always the Equations with no Solution.
In the next session we are going to discuss Equations with no Solution
and Read more maths topics of different grades such as Compound Inequalities
in the upcoming sessions here.