Math Problem Statement

answer and explanation, Solve this math problem show the complete solution. Include what topic this question is.

Simplify: (3a)(4a) / (6(6a^2))

Solution

PIL import Image import pytesseract

Load the image to extract text

image_path = "/mnt/data/17333199998944px6zkg6.jpg" text_from_image = pytesseract.image_to_string(Image.open(image_path))

text_from_imageIt seems the text extraction was incomplete. From the visible content in the image, the problem is:

Simplify: (3a)(4a)/(6(6a2))(3a)(4a) / (6(6a^2))

I will solve it step by step.

Solution:

This is a question from the Simplification of Rational Expressions in Algebra.

  1. Expand the numerator and denominator:

    • Numerator: (3a)(4a)=12a2(3a)(4a) = 12a^2
    • Denominator: 6(6a2)=36a26(6a^2) = 36a^2

    So, the expression becomes: 12a236a2\frac{12a^2}{36a^2}

  2. Simplify by canceling common factors:

    • The a2a^2 in the numerator and denominator cancels out.
    • Simplify the coefficients: 1236=13\frac{12}{36} = \frac{1}{3}.

    Final expression: 13\frac{1}{3}

Answer: A. 13\frac{1}{3}

Would you like further clarifications or related problems? Let me know!


Follow-Up Questions:

  1. What are rational expressions, and how are they simplified?
  2. How do you handle expressions with negative exponents?
  3. How can you verify your simplifications are correct?
  4. What happens when the numerator or denominator equals zero?
  5. How do you simplify expressions with more than one variable?

Tip: Always factorize terms before simplifying to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Rational Expressions

Formulas

Simplification of fractions
Laws of exponents

Theorems

Fundamental principles of rational expressions

Suitable Grade Level

Grades 8-10