Question

Simplify this rational expression: 5x^2+3x-11/x+3 what is the quotient and remainder

Answer 1

After diving, we're left with the quotient of 5x - 12 + (25/(x + 3))

The remainder is 25.

Answer 2

Answer with explanation:

The given rational expression is:

`=(5x^2+3 x-11)/(x+3)\\\\=(5x^2+15 x-12 x-36+36-11)/(x+3)\\\\=(5x*(x+3)-12* (x+3)+25)/(x+3)\\\\=((5x-12) * (x+3)+25)/(x+3)\\\\= 5x-12 +(25)/(x+3)`

Use Euclid Division Algorithm to solve this ,which states that, if a and b are two expressions, when a divided by b, gives remainder m and Quotient g, then by the application of Division theorem , it can be written as:

⇒ a = b g +m, where, 0≤m<g

⇒5 x²+3 x-11=(5 x-12)(x+3)+25

Quotient = 5 x -12

Remainder =25