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:

    $=\frac{5x^2+3 x-11}{x+3}\\\\=\frac{5x^2+15 x-12 x-36+36-11}{x+3}\\\\=\frac{5x\times(x+3)-12\times (x+3)+25}{x+3}\\\\=\frac{(5x-12) \times (x+3)+25}{x+3}\\\\= 5x-12 +\frac{25}{x+3}$

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