Question

(6v^3+42v)/(2v^2+26v+84)

Answer 1

Answer:
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The simplied version is:
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                " $\frac{3v(v^2+7)}{(v^2+13v+42)}$  "  ;

or; write as:  " $\frac{3v(v^2+7)}{(v+7)(v+6)}$  " .
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Explanation:
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Given:
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     " $\frac{6v^3 +42 v}{2v^2 +26v + 84}$  " ;
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     →  Factor out a "6v"$\frac{6v(v^2+7)}{2(v^2+13v+42)}$ in the "numerator"; & factor out a "2" in the denominator;  as follows:
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→ $\frac{6v(v^2+7)}{2(v^2+13v+42)}$ ;
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→  " $\frac{3v(v^2+7)}{(v^2+13v+42)}$ " ;
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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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→  " $\frac{3v(v^2+7)}{(v+7)(v+6)}$ " .
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