((3x^(3)-2x^(2)-19x-6)/(3x+1))
Factor the polynomial using the rational roots theorem.
(((x+(1)/(3))(x+2)(x-3))/(3x+1))
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(((x*(3)/(3)+(1)/(3))(x+2)(x-3))/(3x+1))
Complete the multiplication to produce a denominator of 3 in each expression.
((((3x)/(3)+(1)/(3))(x+2)(x-3))/(3x+1))
Combine the numerators of all expressions that have common denominators.
((((3x+1)/(3))(x+2)(x-3))/(3x+1))
Any number raised to the 1st power is the number.
((((1)/(3))(3x+1)(x+2)(x-3))/(3x+1))
Reduce the expression by canceling out the common factor of (3x+1) from the numerator and denominator.
((<X>(3x+1)<x>(x+2)(x-3))/(<X>(3x+1)<x>)*(1)/(3))
Reduce the expression by canceling out the common factor of (3x+1) from the numerator and denominator.
((x+2)(x-3)*(1)/(3))
Multiply the rational expressions to get ((x+2)(x-3))/(3).
(((x+2)(x-3))/(3))
Remove the parentheses around the expression ((x+2)(x-3))/(3).
((x+2)(x-3))/(3)