Math Problem Statement

stupid maths homwork.pdf

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Solution

It looks like the document you uploaded contains a "Match-Up Simplifying Algebraic Fractions" activity. The task involves simplifying algebraic fractions and matching them to their equivalent forms. Here's a breakdown of a few examples:

Example Breakdown:

  1. x(x+1)(x+1)(x+2)\frac{x(x+1)}{(x+1)(x+2)}: Simplify by canceling x+1x+1 terms, leaving xx+2\frac{x}{x+2}.

  2. 2x2+4x10x\frac{2x^2 + 4x}{10x}: Factor out 2x2x in the numerator, getting 2x(x+2)10x\frac{2x(x+2)}{10x}. Cancel xx and simplify the fraction to 2(x+2)10=x+25\frac{2(x+2)}{10} = \frac{x+2}{5}.

  3. (x1)(x+9)(x+9)(x+4)\frac{(x-1)(x+9)}{(x+9)(x+4)}: Cancel x+9x+9 terms, leaving x1x+4\frac{x-1}{x+4}.

The goal would be to continue simplifying all the algebraic fractions and then find matching triples of equivalent fractions based on their simplified forms.

Would you like help with solving all of the pairs or a specific fraction?

5 Relative Questions:

  1. How do you cancel out common terms in algebraic fractions?
  2. What are some common factoring techniques used in simplifying algebraic fractions?
  3. How do you handle fractions with quadratic expressions in both numerator and denominator?
  4. What role does factoring play in simplifying complex fractions?
  5. What are strategies for recognizing equivalent algebraic fractions?

Tip:

Always check for common factors in both the numerator and denominator before attempting to cancel terms in algebraic fractions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Algebraic Fractions
Factoring
Cancelling Terms

Formulas

Canceling common terms in fractions: \( \frac{x(x+1)}{(x+1)(x+2)} \rightarrow \frac{x}{x+2} \)
Factoring quadratic expressions: \( 2x^2 + 4x \rightarrow 2x(x+2) \)
Simplifying complex fractions: \( \frac{(x-1)(x+9)}{(x+9)(x+4)} \rightarrow \frac{x-1}{x+4} \)

Theorems

Properties of Rational Expressions
Factoring Polynomials

Suitable Grade Level

Grades 9-11