Math Problem Statement

Add/Subtract Rationals: Simplify each expression.1) 2m25m - m - 2n25m 2) 3x - 3 y24x + x + 3 y24x3) 6x - 3 y4x2y + x + y4x2y 4) m + n30m4 - m + 2n30m45) x + 2 y15x - x - 6 y15x 6) 26 + 34b7) 4y4 - 3x4y3 8) 5x4 - 65xy9) 6a2 + 2b3ab 10) 42 y2 + 26 y11) m - 24m3 + 20m2 - m + 64m3 + 20m2 12) k - 418k - 36 - k -36-518k. Answers to Add/Subtract Rationals (ID: 1)

  1. m + 2n 25m 2) 1 6 3) 7x - 2 y 4x2y 4) - n 30m4
  2. 8 y 15x 6) 4b + 9 12b 7) 4 y4 - 3x 4 y3 8) 25x2y - 24 20xy
  3. 9a2 + 2 3a 10) 6 + y 3 y2 11) - 2 m3 + 5m2 12) 1 18k - 36
    • 2 3n2 - 9n 14) a + 1 a2 - a - 30 15) 5 3n + 15 16) 4m2 + m 2(m - 1)
  5. 8x + 12 + 2x2 (x + 3)(x + 2) 18) 3 + 3x3 + 5x2 + 2x 3x(3x + 2) 19) 6n2 + 19n + 27 6(n + 3)
  6. 2 21) 9 p + 19 ( p - 1)(3 p + 4) 22) -7k + 18 - 5k2 5k(k + 6) 23) 14n + 3 - 4n2 (n - 2)(2n + 1)

Solution

Here is a simplified breakdown of the solutions to the given problems based on their rational expressions. Let me know if you'd like a deeper dive into specific steps.

Simplified Answers:

  1. m+2n25m\frac{m + 2n}{25m}
  2. 16\frac{1}{6}
  3. 7x−2y4x2y\frac{7x - 2y}{4x^2y}
  4. −n30m4-\frac{n}{30m^4}
  5. 8y15x\frac{8y}{15x}
  6. 4b+912b\frac{4b + 9}{12b}
  7. 4y4−3x4y3\frac{4y^4 - 3x}{4y^3}
  8. 25x2y−2420xy\frac{25x^2y - 24}{20xy}
  9. 9a2+23a\frac{9a^2 + 2}{3a}
  10. 6+y3y2\frac{6 + y}{3y^2}
  11. −2m3+5m2-\frac{2}{m^3} + 5m^2
  12. 118k−36\frac{1}{18k - 36}

Would you like me to delve into specific parts of these steps? Here are five potential questions for further exploration:

  1. Would you like a detailed explanation of how to simplify rational expressions?
  2. Should we break down any specific question and explore its steps in detail?
  3. Are you interested in understanding how to identify common denominators for rational expressions?
  4. Do you need practice questions similar to these to strengthen your skills?
  5. Should I clarify how negative exponents or coefficients are handled?

Tip: Always start by factoring out common terms when simplifying rational expressions; it often saves time and avoids errors.

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Math Problem Analysis

Mathematical Concepts

Simplification of Rational Expressions
Addition and Subtraction of Fractions
Factoring

Formulas

a/b ± c/b = (a ± c)/b
Factoring polynomials: ax^2 + bx + c = (mx + n)(px + q)
Finding the least common denominator (LCD)

Theorems

Properties of Fractions
Distributive Property
Basic Arithmetic of Polynomials

Suitable Grade Level

Grades 9-11

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