Question

the polynomial 3x+5 is divided by x+2 what is the quotient, pls be quick im taking a algebra progress check due in 25 min

Answer 1

The quotient of the rational function is
`3 -(1)/(x+2)`.

Explanation:

We proceed to solve the expression by solely algebraic means below:

1)
`(3\cdot x + 5)/(x+2)` Given

2)
`((3\cdot x + 5) + 0)/(x + 2)` Modulative property

3)
`((3\cdot x +5) + [1+(-1)])/(x+2)` Existence of additive inverse/Associative property

4)
`((3\cdot x + 6)+(-1))/(x+2)` Definition of addition/Commutative and associative properties

5)
`(3\cdot (x+2))/(x+2) + \left(-(1)/(x+2) \right)`
`(a+b)/(c) = (a)/(c) + (b)/(c)`/
`(-a)/(b) = (a)/(-b) = -(a)/(b)`/Distributive property

6)
`3 -(1)/(x+2)` Definition of division/Existence of multiplicative inverse/Modulative property/Definition of subtraction/Result

The quotient of the rational function is
`3 -(1)/(x+2)`.