Answer with explanation:
The given rational expression is:
[tex]=\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}[/tex]
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
