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Higher Algebra Hall & Knight Partial Fractions (Chapter 23) Solutions

Hall & Knight Higher Algebra Solutions for Chapter 23 ‘Partial Fractions’ are an ideal study material to learn the concept of partial fractions for JEE and NEET. These solutions will help you revise all the questions in the exercises of this chapter, besides imparting complete conceptual clarity in the topics. In this chapter of Higher Algebra by Hall and Knight, you will learn the steps for the decomposition into partial fractions. This chapter is also very crucial as it covers the application of partial fractions in the expansion of different algebraic expressions.

Hall & Knight Algebra Mathematics book with solutions Partial Fractions includes 26 questions in the exercise. This exercise will help you solve partial fractions when the factors of the denominator are all linear and distinct i.e., non-repeating, when the factors of the denominator are all linear but some are repeated, when the denominator contains irreducible quadratic factors which are non-repeated and when the denominator has repeated Quadratic factors. Solving the questions in the exercise of Hall and Knight Higher Algebra Solutions Chapter 23 ‘Partial Fractions’ will give you new insights on how to work on the problems related to this concept in the right way during exams.

Higher Algebra by Hall & Knight Partial Fractions is covered thoroughly by the Instasolv experts in the set of answers. These answers have been prepared after extensive research on the problems and most frequently raising doubts. These solutions have been made interactive and inclusive with the help of various techniques such as the use of simple and understandable language and the use of flowcharts and diagrams wherever necessary. 

Important Topics for Hall and Knight Higher Algebra Solutions Chapter: 23 Partial Fractions

Introduction

When there is a group of fractions divided into a group of simpler or partial (as we may term it) fractions through a positive or a negative sign, we can collect it into one fraction in which the denominator is the lowest common denominator of all fraction.

Whereas when we have to separate a given fraction into smaller entities or partial fractions, we follow the opposite process.

According to the treatises on the Integral Calculus, it can be proved that any rational fraction can be segregated into a series of partial fractions with a linear factor for a linear fraction in the denominator in the form Ax-a For a quadratic expression x2+px+q, the corresponding partial fraction will be of the form Px+Qx2+px+qHere, the quantities, A, P, Q, and so on are independent of x. 

Use of Partial Fractions in the Expansion of Series

We can expand resolve any algebraic expression into the partial fractions and use the results for expansion of any given rational fraction in the increasing powers of x. The general term of expansion is written by observing the pattern that the expanded series follows. 

In some cases the general term, if denoted by r, can also vary if r is even or when r is odd. Such questions are scoring and frequently recurring in the competitive exams such as JEE etc.

Exercise Discussion of Hall and Knight Higher Algebra Solutions Chapter 23: Partial Fractions

  1. Exercise 23 has been divided into various sections covering each topic in a detailed manner.
  2. The first section will require you to resolve the given fractional algebraic expressions into partial fractions.
  3. The second section comprises of questions in which you will have to find the general term when the expressions are expanded in the ascending powers of x.
  4. You will learn to find the sum of the n terms in a given series (including infinite series) in the exercise questions of this chapter. 
  5. Lastly, in this chapter, you will get to prove some important results related to the homogeneous products of ‘n’ dimensions.

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