perform the indicated operations and express the answers in simplified form. (11x−3)2−(6x+5)3

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perform the indicated operations and express the answers in simplified form.  (11x−3)2−(6x+5)3

SabadisO · Accepted Answer

Step 1 The Addition and subtraction between rational functions (fractional form of functions) can be done by converting both fractions denominators to the same value and then performing the operations. Using cross multiplication or by using LCM method we can convert the fractions to same denominator Step 2 Consider the rational expression (11x−3)2−(6x+5)3 Let us use the LCM technique to solve rational expressions, Using LCM technique , we have to find the LCM of the denominators and we need to convert both the denominators to LCM value by multiplying both numerator and denominator by suitable constant expression . Here the LCM of the denominators 2 and 3 is 6 (2.3=6) Now let us convert both the denominators to 6 , (11x−3)2−(6x+5)3=(11x−3)2×33−(6x+5)3×22 =3(11x−3)−2(6x+5)6 { now we have same denominator , combining fractions} Now we can simplify the numerator by multiplying terms and the regrouping and subtracting the terms, 3(11x−3)−2(6x+5)6=33x−9−12x−106 =33x−12x−9−106 =21x−196 Hence we have the simplest rational form 21x−196

perform the indicated operations and express the answers in simplified form.

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