How do you express the quotient of (3x^2+13x+4)/((3x+1)/5)3x2+13x+43x+15 in simplest form?

1 Answer
José F.
Apr 15, 2016

5x+20, x!=-1/35x+20,x≠−13

Explanation:

(3x^2+13x+4)/((3x+1)/5)=(3x^2+13x+4)-:(3x+1)/5=(3x^2+13x+4)xx5/(3x+1)3x2+13x+43x+15=(3x2+13x+4)÷3x+15=(3x2+13x+4)×53x+1

=5((3x^2+12x)+(x+4))/(3x+1)=5(3x(x+4)+(x+4))/(3x+1)=5(cancel((3x+1))(x+4))/cancel(3x+1)=5x+20, x!=-1/3

When 3x+1=0 you obtain 0/0 in the full formula, while in simplified it is 55/3. The statement x!=-1/3 must be included to guarantee both full and simplified expressions are equivalent in their domains.

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