Explanation Given: The rational expression is, 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 . Property used: Fundamental property, P Q = P S Q S , for all mathematical expressions P , Q , R , and S , with Q ≠ 0 and S ≠ 0 . Subtraction property, P Q − R Q = P − R Q , for all mathematical expressions P , Q , and R , with Q ≠ 0 . Calculation: Since the denominators of the two rational expressions are different, take least common denominator and then add the numerator while keeping the same denominator. Obtain the factors of the denominators. 2 k 2 + 3 k − 2 = 2 k 2 − k + 4 k − 2 = k ( 2 k − 1 ) + 2 ( 2 k − 1 ) = ( 2 k − 1 ) ( k + 2 ) 2 k 2 − 7 k + 3 = 2 k 2 − k − 6 k + 3 = k ( 2 k − 1 ) − 3 ( 2 k − 1 ) = ( 2 k − 1 ) ( k − 3 ) Thus, the rational expression becomes, 3 k ( 2 k − 1 ) ( k + 2 ) − 2 k ( 2 k − 1 ) ( k − 3 ) . The least common denominator of ( 2 k − 1 ) ( k + 2 ) and ( 2 k − 1 ) ( k − 3 ) is ( k + 2 ) ( 2 k − 1 ) ( k − 3 ) . Multiply the first term by ( x − 2 ) ( x − 2 ) and the second term by ( x + 3 ) ( x + 3 ) and apply Fundamental property as follows. 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 = 3 k ( 2 k − 1 ) ( k + 2 ) − 2 k ( 2 k − 1 ) ( k − 3 ) = 3 k ( 2 k − 1 ) ( k + 2 ) ⋅ ( k − 3 ) ( k − 3 ) − 2 k ( 2 k − 1 ) ( k − 3 ) ⋅ ( k + 2 ) ( k + 2 )

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

See similar textbooks

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter R.3, Problem 35E

To determine

To express: The rational expression 3k2k2+3k−2−2k2k2−7k+3 in lowest terms.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter R.3, Problem 34E

Chapter R.3, Problem 36E

Students have asked these similar questions

4 7 1 k 3.

Subtract. 3. b²+7b+12 b² + 5b + 6 9G + ,9 b+7b+12 b +5b +6 (Simplify your answer.)

5.) A number y is multiplied by -0.8. The product is -49. What is the value of y?

Chapter R Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. R.1 - Perform the operation 3(x24x5)4(3x25x7)Ch. R.1 - Perform the operation (3y+2)(4y22y5).Ch. R.1 - Find (2x+7)(3x1) using the FOIL method.Ch. R.1 - Find (3x+2y)3.Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To express: The rational expression 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 in lowest terms.

Solution Summary: The author explains the rational expression, 2k2, in lowest terms, with the least common denominator and subtraction property.

Concept explainers

Videos

To express: The rational expression 3k2k2+3k−2−2k2k2−7k+3 in lowest terms.

Want to see the full answer?

Chapter R Solutions