SOLUTION: 1- indicates the quotient and remainder 8x^3+4x-5 --------- 2x+1 2- simplify the following radical expression: 3+√5 ----- √7-√3 x^3-y^3 y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1- indicates the quotient and remainder 8x^3+4x-5 --------- 2x+1 2- simplify the following radical expression: 3+√5 ----- √7-√3 x^3-y^3 y      Log On


   

Question 1135698: 1- indicates the quotient and remainder

8x^3+4x-5
---------
2x+1

2- simplify the following radical expression:
3+√5
-----
√7-√3


x^3-y^3 y^2+2xy+x^2
-------- X -----------
2x^2-2y^2 x^2+xy+y^2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1- indicates the quotient and remainder
%288x%5E3%2B4x-5%29%2F%282x%2B1+%29...use long division
..............(4x%5E2-2x%2B3
2x%2B1..|8x%5E3%2B0%2Ax%5E2%2B4x-5
.....................8x%5E3%2B4x%5E2....subtract
...............................-4x%5E2%2B4x
.................................-4x%5E2-2x....subtract
............................................6x-5
.............................................6x%2B3....subtract
.................................................-8
the quotient is 4x%5E2-2x%2B2
and remainder is -9
%288x%5E3%2B4x-5%29%2F%282x%2B1+%29=%284x%5E2-2x%2B3%29%282x%2B1+%29-8


2- simplify the following radical expression:
%283%2Bsqrt%285%29%29%2F%28sqrt%287%29-sqrt%283%29%29...multiply both numerator and denominator by %28sqrt%287%29%2Bsqrt%283%29%29



%283sqrt%287%29%2Bsqrt%2835%29%2B3sqrt%283%29%2Bsqrt%2815%29%29+%2F4-> exact solution
if we go further approximate solution is 5.7306

3-








%281%2F2%29%2A%28%28+y%2Bx%29%2F1%29

%28+y%2Bx%29%2F2