- #1
Kifsif
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Simplify the expression (need hint)
- Thread starter Kifsif
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The discussion focuses on simplifying the expression (4b^4 + 4ab^2 + a^2):(2b^2 + a). The initial simplification leads to 2b^2 + a, but further progress is needed. A hint suggests factoring the right term to find two roots that create relationships between a and b, which may lead to cancellations in the overall expression. Additionally, the case where 2a equals b is highlighted as potentially revealing further simplifications. The final expression after applying these hints is expected to be (b^2 + b + ab + a)/(b^2 - ab - 2a^2).
- #2
- 42,783
- 10,488
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 
)
\frac{b^2+b+ab+a}{b^2-ab-2a^2}.
) \frac{b^2+b+ab+a}{b^2-ab-2a^2}.
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