Answer:
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The simplied version is:
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" [tex] \frac{3v(v^2+7)}{(v^2+13v+42)} [/tex] " ;
or; write as: " [tex] \frac{3v(v^2+7)}{(v+7)(v+6)} [/tex] " .
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Explanation:
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Given:
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" [tex] \frac{6v^3 +42 v}{2v^2 +26v + 84} [/tex] " ;
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→ Factor out a "6v"[tex] \frac{6v(v^2+7)}{2(v^2+13v+42)}[/tex] in the "numerator"; & factor out a "2" in the denominator; as follows:
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→ [tex] \frac{6v(v^2+7)}{2(v^2+13v+42)}[/tex] ;
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→ " [tex] \frac{3v(v^2+7)}{(v^2+13v+42)} [/tex] " ;
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or; factor out the "denominator" :
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→ (v² + 13v + 42) = (v+7)(v+6) ;
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and write as:
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→ " [tex] \frac{3v(v^2+7)}{(v+7)(v+6)} [/tex] " .
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