Exercise 4.2 - 10 Class Math - Part 1 | Waqas Nasir
Waqas Nasir・45 minutes read
Understanding the distinctions between exercises 4.1, 4.2, and 4.3 is crucial in solving fraction-related problems, especially in converting fractions into partial fractions. The text highlights the process of assigning values to unknowns 'a', 'b', and 'c' to convert fractions with repeated factors, ultimately determining the partial fractions for the given equation.
Insights
- Understanding the differences between exercises 4.1, 4.2, and 4.3 in solving fraction-related questions is crucial, with Exercise 4.2 focusing on repeated factors in the denominator, while Exercise 4.1 deals with non-repeated factors.
- Converting fractions into partial fractions is essential in solving fraction-related questions, involving the separation of factors and assigning unknown values to solve repeated factors, ultimately leading to the calculation of 'a', 'b', and 'c' values for the partial fractions.
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Recent questions
How are fractions converted into partial fractions?
Fractions are converted by separating factors and assigning unknown numbers to solve repeated linear factors.
What is the difference between exercises 4.1, 4.2, and 4.3?
Exercise 4.1 deals with non-repeated factors, 4.2 focuses on repeated factors, and 4.3 involves converting improper fractions.
How are unknown values determined in fraction equations?
Unknown values (a, b, c) are found by substituting specific values for x in equations and solving for the variables.
What is the process of converting an improper fraction?
Improper fractions are converted using long division, resulting in a proper fraction in the form of 'Ksh + remainder/divisor'.
How are partial fractions calculated for a given equation?
Partial fractions are calculated by determining the values of 'a', 'b', and 'c' through a series of calculations and substituting them back into the equation.
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Summary
00:00
Understanding and Solving Fraction Exercises 4.1-4.3
- The text discusses the importance of understanding the differences between exercises 4.1, 4.2, and 4.3 in solving fraction-related questions.
- It emphasizes the need to convert fractions into partial fractions within the four exercises.
- Exercise 4.2 focuses on identifying repeated factors in the denominator of fractions.
- In contrast, Exercise 4.1 deals with non-repeated factors in fractions.
- The text explains that linear factors with a power of one are considered non-repeated.
- It highlights the method to solve questions with repeated linear factors, distinguishing them from non-repeated ones.
- The process involves separating factors and assigning unknown numbers to solve the repeated factors.
- The text provides a detailed example of converting a fraction with repeated linear factors into partial fractions.
- It outlines the steps to find the values of unknowns (a, b, c) by substituting specific values for x in the equations.
- The text concludes by demonstrating the calculation process to determine the values of a, b, and c in the given fraction equation.
16:31
Multiplying Numbers to Find Zero and One
- Multiplying a positive 2 and a negative 2 results in zero.
- When both numbers are multiplied by zero, they become zero.
- The value of 'a' becomes zero in this scenario.
- Similarly, the value of 'b' also becomes zero.
- Multiplying 'c' by zero results in 'c' becoming zero.
- The square of one is one.
- The value of 'c' is determined to be -1.
- The value of 'a' is found using equation 2.
- The values of 'a', 'b', and 'c' are calculated.
- The partial fraction is determined based on the values of 'a', 'b', and 'c'.
38:43
Partial Fractions: Coefficients, Equations, and Solutions
- The coefficient of x in the equation is denoted as 'c - 1'.
- By substituting c = -1 in equation one and three, the value of a is determined to be 'r'.
- The required partial fraction R is calculated by dividing a by b/(x+2)^2, b by x+2, and c by x+3.
- The value of b is found to be 2, and c is determined to be 1.
- Expanding equation two, the expression 9 = ax^2 + (a+c)x + (a+b+4c) is derived.
- The values of a, b, and c are obtained as -1, 2, and 1 respectively.
- The partial fractions are identified as -1/(x+2), 2/(x+2)^2, and 1/(x-1).
- The conclusion presents the partial fractions as -1/(x+2), 2/(x+2)^2, and 1/(x-1).
- The process of converting an improper fraction into a proper fraction is explained using long division.
- The final step involves writing the solution in the form of 'Ksh + remainder/divisor'.
58:49
Dividing x4 + 1 to find factors
- The process involves dividing x4 + 1 by a divisor, which is identified as D in the equation.
- The divisor D results in xK - a value that is crucial for further calculations.
- By converting the expression into factors and eliminating denominators, two equations are derived.
- The value of b is determined to be -1 through a series of calculations.
- The values of a, b, and c are found to be -1, -1, and 2 respectively, leading to the required partial fractions for the given equation.
