Rational Expressions Calculator Rational Expressions Calculator
Rational expression is a collection of many Rational Numbers variables which is collected by arithmetic operations like we have two rational variables like 3x3 + 2x2 5x – 4 and -3x3 + 7x2 + 2x – 8 and when we define these two rational numbers variable in numerator and denominator form like, (3x3 + 2x2 - 5x – 4) / (-3x3 + 7x2 + 2x – 8) is called as a rational expression. Now we discuss rational expressions calculator with steps: We use following steps to solve a rational expression with the help of rational expression calculator Step 1: First of all, we find out factors from numerator and denominator like when we evaluate above rational expression R = (3x3 + 2x2 - 5x – 4) / (-3x3 + 7x2 + 2x – 8), Then, we find out factors of numerator 3x3 + 2x2 - 5x – 4 and denominator, -3x3 + 7x2 + 2x – 8,
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Factor of numerator 3x3 + 2x2 - 5x – 4 = (x + 1)2 (3x – 4), and factors of denominator -3x3 + 7x2 + 2x – 8 = -(x + 1) (x – 2) (3x – 4). Step 2: After evaluation of factors, now we put factors in given rational expression R =(3x3 + 2x2 - 5x – 4) / (-3x3 + 7x2 + 2x – 8), => R = [(x + 1)2 (3x – 4) / -(x + 1) (x – 2) (3x – 4)]. Step 3: After first two steps, we cancel any common terms, which shows match between numerator and denominatorR = [(x + 1)2 (3x – 4) / -(x + 1) (x – 2) (3x – 4)], => R = (x + 1) / -(x – 2), So, final answer of rational expression is (x + 1) / - (x – 2). Rational numbers can form expressions when we join Rational Numbers with various mathematical operators namely addition, subtraction, multiplication and division. Rational Numbers are the numbers which are written in form of p/q, where p and q are integers, and q≠ 0. In this, p is the numerator and q is the denominator. Always remember all natural, whole numbers, integers including zero(0) are all the members of the family of rational numbers because they all have 1 as the denominator, which is not 0. Two rational numbers can be added like the addition procedure of simple fractions and follow the laws of addition of integers. Let us take an example in order to understand the concept, Read More About Verifying Trigonometric Identities Worksheet Tutorcircle.com
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Now, we talk about the division of one rational number by another. Before studying about division, we should know about the reciprocal of numbers. Reciprocal of a rational number means to divide 1 by the given rational number, i.e. reciprocal of 4 is 1 /4. Also Reciprocal of -4/5 = 1÷ (-4/5) If more than one operator exists in the given expression, then we apply the Laws of BODMAS to solve the expressions of rational numbers, where 'B'- 'Brackets', 'O'- 'Of operation', 'D'- 'Division', 'M'- 'Multiplication', 'A'- 'Addition', 'S'- 'Subtraction'. Define Rational Expression For defining rational expression we can say that a rational number is any number in the form of p/q, where p and q are real numbers but q can never be zero as we can’t divide any real number with zero. We can also define rational expressions as a polynomial in the form of p/q + a/b where a and p, q, a and b are rational number and q and b can't be zero.
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