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Iske first question Ka 4th question ho samajhao

The fourth sub-question of the first question (i.e., the fourth part of the "Add the following polynomials") is as follows:

\[
\frac{4}{3}x^2 + \frac{5}{4}x + \frac{2}{3} - \frac{5}{3}x^2 + \frac{4}{3}x + 1
\]

### Step-by-Step Solution:

1. **Group the like terms**:
   - Combine the terms with \(x^2\): 
     \[
     \frac{4}{3}x^2 - \frac{5}{3}x^2 = \frac{-1}{3}x^2
     \]
   - Combine the terms with \(x\): 
     \[
     \frac{5}{4}x + \frac{4}{3}x
     \]
     To combine these, we need a common denominator. The least common denominator of 4 and 3 is 12, so we rewrite the terms:
     \[
     \frac{5}{4}x = \frac{15}{12}x, \quad \frac{4}{3}x = \frac{16}{12}x
     \]
     Now, add them:
     \[
     \frac{15}{12}x + \frac{16}{12}x = \frac{31}{12}x
     \]
   - Combine the constant terms:
     \[
     \frac{2}{3} + 1 = \frac{2}{3} + \frac{3}{3} = \frac{5}{3}
     \]

2. **Final Answer**:
   After combining all the like terms, the final simplified polynomial is:
   \[
   \frac{-1}{3}x^2 + \frac{31}{12}x + \frac{5}{3}
   \]

Would you like further details or have any other questions? Here are 5 related questions to further explore:

1. How do you simplify polynomials involving multiple variables?
2. What is the method to find the least common denominator when combining fractions?
3. Can you explain how to add or subtract terms in polynomials with different powers?
4. How do you multiply polynomials with fractional coefficients?
5. What is the importance of grouping like terms in algebraic expressions?

**Tip:** When combining fractions, always find the least common denominator to make the addition or subtraction easier.

Add the following polynomials: \(\frac{4}{3}x^2 + \frac{5}{4}x + \frac{2}{3} - \frac{5}{3}x^2 + \frac{4}{3}x + 1\)

This page explains how to add polynomials with fractions step-by-step. The example involves grouping like terms, handling fractional coefficients, and simplifying the expression. Suitable for students in Grades 8-10.

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