Answer:
B..... Ax+B/5x^2+1 + Cx+D/(5x^2+1)^2
Step-by-step explanation:
Trust got it right on edge
The quotient and remainder, written as partial fractions, of 15x^2+52x+43/3x^2+5x-8 would be [tex]\dfrac{A}{(3x + 8)} + \dfrac{B}{(x-1)}[/tex] where A is -8/3 and B is 1.
We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
[tex]\dfrac{15x^2+52x+43}{3x^2+5x-8}\\\\\\\dfrac{15x^2+52x+43}{3x^2+(8-3)x-8}\\\\\\\dfrac{15x^2+52x+43}{3x^2+8x-3x-8}\\\\\\\dfrac{15x^2+52x+43}{3x(x -1)+8(x - 1)}\\\\\\\dfrac{15x^2+52x+43}{(3x + 8)(x - 1)}[/tex]
[tex]\dfrac{A}{(3x + 8)} + \dfrac{B}{(x-1)}[/tex].
To find the value of A;
3x + 8 = 0
x = -8/3
To find the value of B;
x - 1 = 0
x = 1
Therefore, The quotient and remainder, written as partial fractions, of 15x^2+52x+43/3x^2+5x-8 would be [tex]\dfrac{A}{(3x + 8)} + \dfrac{B}{(x-1)}[/tex] where A is -8/3 and B is 1.
Learn more about quotient;
https://brainly.com/question/23398786
#SPJ2
