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Simplification of Rational Expressions

TopIn order to learn about the simplification of rational expressions, we must remember that all the mathematical operators, namely addition, subtraction, multiplication and division can be performed on the Rational Numbers. First thing we must check while adding or subtracting the rational numbers is that is the denominator same? If yes, then simply we are going to add or subtract the numerators and then convert the resultant rational number into the simplest and standard form. On the other hand if we have to perform addition or subtraction between the two rational numbers, such that the denominators of the two rational numbers is not same, then in that case, we will first take the lcm of the two denominators and then we will convert the two numbers in their equivalent form, such that the denominator becomes the lcm of the two numbers. We can now perform the desired operation.
Now we look at how to perform the multiplication between the two rational numbers. For finding the product, we will simply multiply the numerator with the numerator and the denominator is multiplied with the denominator. The result so obtained is now converted into the standard form. Here we must remember two things; firstly if any rational number is multiplied with 0, the resultant rational number is also zero. Secondly, if any rational number is multiplied with 1, the result is the original rational number itself.
While finding the quotient of the two rational numbers, when we divide the first rational number with other rational number, then the operation of division is changed into multiplication and the reciprocal of the divisor is written. Now it becomes the ordinary sum of the multiplication. The product so obtained becomes the quotient of the two numbers. We must always remember that if any number is divided by 1, the result is the dividend itself.