Rational Expression Word Problems Rational Expression Word Problems
The rational expression is an expression which is expressed in from of two integers. The rational expression is rational because one integer is divided by the second one. This is the definition of rational number where denominator is nonzero real number. If m and n are two integer then it can be written as fraction m/n and n is not equal to zero. There are many types of expression which are performed on the basis of rational expression and these are basic arithmetic operations like addition, subtraction, multiplication and division. There is a property of rational expressions, when we perform any arithmetic operations on the two rational expressions then the result of those rational expressions always gives another rational expression. Let us suppose that A = p/q and B = r/s be two rational expressions, where p, q, r, and s are the integers. Know More About Rational Number Worksheets
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Now the product of these two rational expression that is AB = pr / qs and the division of these rational expression is A / B = ps / qr. When we are doing addition and subtraction of rational expressions, then it is compulsory to factor the denominator of each and every rational expression. We add or subtract one in fractions and calculate the least common multiple in the denominators, then rewriting each and every fraction in that denominator and lastly we adding the numerators. On other hand when we multiply and divide two rational expressions then it is necessary to factor the numerator of the rational expression and also denominator of that rational expression. Rational expressions word problems utilize this concept. f1= (x+4) / (x+1) and f2= (x+6) / (x-2): product of these rational expression is (x+4) (x+6) / (x+1) (x+2). Next we are doing the division by follow the above rule (x+4) (x2) / (x+1) (x+6). Now the addition and subtraction of the given rational expression follows the above rule of addition and subtraction that is first we factor the both rational expressions if there is any need for that, if there is no need to factor then we will solve the rational expression as per the given rule. Now come on the example, here two rational expressions are given in the factor form so here no need of factorization. But here is one more condition that we will find the least common denominator of given rational expression. Their addition/subtraction will be [(x+4)(x-2)±(x+1)(x+6)]/(x+1)(x-2) Read More About What Is A Rational Number
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Rational expressions applications word problems: Example- Assume that Mary takes 6 hours to work alone and Ruby takes 8 hours to do the same work alone. How long will it take them to complete the job if they work together? Solution: Let A be the amount of time it takes to complete the job together. Rate of work of Mary=1/6 Rate of work of Ruby=1/8 => In A hours, Mary and Ruby do A/6 and A/8 amount of work respectively. => If they work together: A/6 +A/6=1 Thus they will complete the job in 24/7 hours.
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