Explanation Given Information: The rational expression is 2 m m − n − 5 m + n 2 m − 2 n . Formula used: Subtracting Rational Expressions (Different Denominator) There are following steps to add or subtract the rational expressions with different denominators. Step 1: Obtain the least common denominator (LCD) of the rational expression. Step 2: Express rational expression as an equivalent rational expression with the LCD as the denominator of each terms of the expression. Step 3: Numerators are added or subtracted depending upon the sign of the numerator to obtain the resultant numerator. The LCD is the denominator of the rational resultant expression. Step 4: Now, simplify the expression to the lowest terms using the fundamental property. Distributive property: a ( b + c ) = a b + a c Here, a , b and c are real numbers. Calculation: Consider the rational expression. 2 m m − n − 5 m + n 2 m − 2 n Factor out 2 from the denominator of the second fraction. 2 m m − n − 5 m + n 2 m − 2 n = 2 m m − n − 5 m + n 2 ( m − n ) Solve to obtain the LCD of denominator of the fractions that is ( m − n ) and 2 ( m − n ) . On solving the LCD is 2 ( m − n ) . The rational expression is written as a fraction in such a way that the LCD is the denominator of the fraction. 2 m m − n = ( 2 m ) ( 2 ) ( m − n ) ( 2 ) = 4 m 2 ( m − n ) And, 5 m + n 2 ( m − n ) = 5 m + n 2 ( m − n ) Since the fractions have the common denominator, subtract the numerators and the LCD is the denominator

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Chapter 6.4, Problem 67E

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To calculate: The value of the rational expression 2mm−n−5m+n2m−2n in the lowest term.

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Chapter 6.4, Problem 66E

Chapter 6.4, Problem 68E

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The value of the rational expression 2 m m − n − 5 m + n 2 m − 2 n in the lowest term.

Solution Summary: The author explains how to add or subtract rational expressions with different denominators.

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To calculate: The value of the rational expression 2mm−n−5m+n2m−2n in the lowest term.

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