To determine To calculate: The simplified form of the rational expression 4 4 x − 5 y − 3 x 2 + 2 y 2 64 x 3 − 125 y 3 . Explanation Given Information: The provided rational expression is 4 4 x − 5 y − 3 x 2 + 2 y 2 64 x 3 − 125 y 3 . Formula used: Follow the steps as mentioned below to add the rational expression with different denominator. Step1: Find out the least common denominator (LCD). Step2: Rewrite the fractions of the rational expression with LCD, by multiplying and dividing the numerator and the denominator with the terms needed to get LCD. Step3: Simplify the numerator by multiplying the terms and leave the denominator in factor form. Step4: Add or subtract the numerators and keep LCD same. Step5: Simplify the expression obtained from step 4 by factoring the numerator, if possible. Calculation: Consider the rational expression, 4 4 x − 5 y − 3 x 2 + 2 y 2 64 x 3 − 125 y 3 The denominators are 4 x − 5 y and 64 x 3 − 125 y 3 . Take the factors of 4 x − 5 y , 4 x − 5 y = 1 ⋅ ( 4 x − 5 y ) Now take the factors of 64 x 3 − 125 y 3 , 64 x 3 − 125 y 3 = ( 4 x − 5 y ) ( 16 x 2 + 20 x y + 25 y 2 ) Thus, all the factors from the denominators of the rational expression are ( 4 x − 5 y ) , ( 16 x 2 + 20 x y + 25 y 2 ) To compute the LCD take the product of all the non-repeated factors and take repeated factors one time, as, LCD = ( 4 x − 5 y ) ( 16 x 2 + 20 x y + 25 y 2 ) Rewrite the expression in factor forms, 4 4 x − 5 y − 3 x 2 + 2 y 2 64 x 3 − 125 y 3 = 4 4 x − 5 y − 3 x 2 + 2 y 2 ( 4 x − 5 y ) ( 16 x 2 + 20 x y + 25 y 2 ) To make the fractions of the rational expression with LCD, multiply first term of the expression by 16 x 2 + 20 x y + 25 y 2 16 x 2 + 20 x y + 25 y 2 . 4 4 x − 5 y − 3 x 2 + 2 y 2 ( 4 x − 5 y ) ( 16 x 2 + 20 x y + 25 y 2 ) = [ 4 4 x − 5 y ⋅ 16 x 2 + 20 x y + 25 y 2 16 x 2 + 20 x y + 25 y 2 − 3 x 2 + 2 y 2 ( 4 x − 5 y ) ( 16 x 2 + 20 x y + 25 y 2 ) ] Now multiply numerators and keep denominator in factor form, [ 4 4 x − 5 y ⋅ 16 x 2 + 20 x y + 25 y 2 16 x 2 + 20 x y + 25 y 2 − 3 x 2 + 2 y 2 ( 4 x − 5

Intermediate Algebra For College Students (9th Edition)

9th Edition

ISBN: 9780321927354

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 6.2, Problem 74ES

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To calculate: The simplified form of the rational expression 44x−5y−3x2+2y264x3−125y3.

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Chapter 6.2, Problem 73ES

Chapter 6.2, Problem 75ES

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(a) (b) (c) (d) de unique? Answer the following questions related to the linear system x + y + z = 2 x-y+z=0 2x + y 2 3 rewrite the linear system into the matrix-vector form A = 5 Fuse elementary row operation to solve this linear system. Is the solution use elementary row operation to find the inverse of A and then solve the linear system. Verify the solution is the same as (b). give the null space of matrix A and find the dimension of null space. give the column space of matrix A and find the dimension of the column space of A (Hint: use Rank-Nullity Theorem).

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Intermediate Algebra For College Students (9th Edition)

Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Prob. 6ES Ch. 6.1 - Prob. 9ES Ch. 6.1 - Prob. 7ES Ch. 6.1 - Prob. 10ES Ch. 6.1 - Determine the values that are excluded in the...

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