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Exploring Rational Expressions

We know that all the mathematical operations can be performed on the Rational Numbers. We say that the Rational expression is the Mathematical Expression in which we can find the rational numbers combined together with the arithmetical operators.  Lets learn about the rational expressions and the method used to simplify rational expressions.
If two or more rational numbers are joined together with the mathematical operator, it forms the rational expression.  We solve the rational expression in order to get the number in the form of the rational number. When we proceed to solve the rational numbers, with the addition or subtraction operation, we first need to convert the two rational numbers into their equivalent form, such that the denominators of the two rational numbers becomes same and now either the addition of the subtraction operation is performed on the numerators and we get the sum or the difference of the two rational numbers. Now let us say that the operation of multiplication or division is to be performed between the two rational numbers, and then a different method is used.
In case the two numbers are to be multiplied, then we will simply multiply the numerator with the numerator and the denominator is to be multiplied with the denominator. The resultant rational number is then converted into the standard form. To convert the product into the standard form, we will find the HCF of the numerator and the denominator and then divide both the numerator and the denominator by the HCF.
In case of division, we will change the divisor to its reciprocal and then along with it the sign of division will change to the sign of multiplication. Thus it is now the ordinary expression of the multiplication of two rational numbers, which can be solved using the method of multiplication.

Topics Covered in Exploring Rational Expressions

Graphing Rational Function

Rational function can be defined as Ratio of two Polynomials. In Rational Function numerator and denominator values are present, denominator value of rational function cannot be zero. In other words rational function can be defined as ratio of two polynomials. For example: p2 + 5 / p + 2, as it is the ratio of two polynomials. Now we will see Graphing rational...Read More

Add and Subtract Rational Expression

Rational expression can be defined as a function which is given as Ratio of two Polynomials. In other words, rational expression can be expressed as a fraction which is comprised of numerator and denominator, where as numerator is the upper part of ratio and denominator is lower part.
Let’s consider a function f (y) which is represented as:
f (y) =...Read More

Inverse Variation

Statements of the inverse variations can be stated as follows:
Suppose we have two variables: “a” and “b” such that,
1.    Value of “b” differs inversely as that of “a”,
2.    “b” is inversely proportional to “a”.
Actual relation can be written as:
b = f a, where 'f' is some fixed real number and not equals to zero. “f” is also known as variation constant or prop...Read More

Indirect Variations

Indirect variations are exactly opposite of Direct Variations. In direct variations we study that two variables are directly proportional to each other but here in indirect variations, variables are inversely proportional to each other. For example, relation between two variables values like speed and time have an inverse relation as when speed increases the time dec...Read More

Direct Variations

Two variable quantities in Math are said to be in direct variation if, proportion of their values does not change.
For instance, suppose we have two variables “a” and “b” such that they are in a relation a = 4b i.e. value of “a” will always be four times the corresponding value of “b” or we can say that the values of “a” and “b” are in a fixed Ratio 1 / 4.  That is, i...Read More

Solving Rational Equations

Solving a rational equation is very similar to solving normal mathematical equation. Rational equation is in the form of p / q where one of them can be unknown variable. Let us see how to solve rational equations.
As we studied above that rational equations contain terms in Ratio form. For Example: 4 / x + 7 = 2 / 3x is a rational equation because it has x in...Read More

Multiply and Divide Rational Expression

Rational expression is in the form of p / q. Here p and q are two real expressions. We can perform arithmetic operations on rational expressions such as addition, subtraction, multiplication and division. Let us discuss multiplying and dividing rational expressions.

For multiplication we need two rational expressions. Rational expression has nu...Read More

Further Read

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