Express the quotient in simplest form 3^2+13x+4/(3x+1/5) a) (x+4) b) 5(x-4) c) (5x+4) d) 5(x+4)

D) 5(x+4)

Step-by-step explanation:

The quotient is the result of the division of the numerator by the denominator but first the denominator has to be simplified.

Then the numerator is factorized. The factor common between the numerator and denominator is ascertained and eliminated.

Hence

3x^2+13x+4/(3x+1/5)

= 3x^2+13x+4 ÷ 3x+1/5

= 5(3x^2+13x+4)/(3x+1)

= 5(3x^2+12x + x+4)/(3x+1)

= 5(x + 4)(3x + 1)/(3x + 1)

= 5(x + 4)

the first option is the answer.