- #1
Kifsif
- 1
- 0
Simplify the expression (need hint)
- Context: High School
- Thread starter Kifsif
- Start date
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- Expression Simplify
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SUMMARY
The discussion focuses on simplifying the expression (4b4 + 4ab2 + a2):(2b2 + a) and highlights the simplification to 2b2 + a. Participants suggest factoring the right-hand term to identify roots that could lead to cancellations in the overall expression. The hint provided emphasizes the significance of substituting specific relationships, such as 2a = b, to explore further simplifications. Ultimately, the goal is to convert fractions to a common denominator to achieve cancellation.
PREREQUISITES- Understanding of algebraic expressions and simplification techniques
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- Knowledge of finding roots of equations
- Ability to manipulate fractions and common denominators
- Practice factoring polynomials using techniques such as grouping and the quadratic formula
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- Explore methods for manipulating fractions, including finding common denominators
- Investigate advanced algebraic concepts such as rational expressions and their simplifications
Students preparing for university-level mathematics, educators teaching algebra, and anyone looking to enhance their skills in simplifying algebraic expressions.
- #2
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Can you factorise the term on the right? Having factorised it, that gives you two 'roots', i.e. Relationships between a and b that would make that term vanish. Try substituting those, in turn, in denominators elsewhere to see if there's some cancellation. Likewise, the case 2a=b looks interesting. See what other terms vanish for that combination.
- #3
Xarx
- 7
- 0
You have to convert the upper fractions to a common denominator. Then you'll find that the numerator cancels out with part of the denominator. You'll get (I hope 
)
[itex]\frac{b^2+b+ab+a}{b^2-ab-2a^2}[/itex].
) [itex]\frac{b^2+b+ab+a}{b^2-ab-2a^2}[/itex].
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