SOLUTION: 1/(2(x+3))+(x/4) = (2x)/(x^2+3x+2) Write the equation as a polynomial p(x)=0. Show that the polynomial p(x) on the left side of the equation is the square of a trinomial in the fo

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1/(2(x+3))+(x/4) = (2x)/(x^2+3x+2) Write the equation as a polynomial p(x)=0. Show that the polynomial p(x) on the left side of the equation is the square of a trinomial in the fo      Log On


   

Question 388889: 1/(2(x+3))+(x/4) = (2x)/(x^2+3x+2)
Write the equation as a polynomial p(x)=0. Show that the polynomial p(x) on the left side of the equation is the square of a trinomial in the form x^2+bx+c. Find the solutions to the equation.
I tried to solve this with an LCD of 4(x+3)(x+2)(x+1) but I can't get the equation into quadratic form.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
using your LCD ___ 2(x^2 + 3x + 2) + [(x^2 + 3x)(x^2 + 3x + 2)] = 8x(x + 3)

2(x^2 + 3x) + 4 + (x^2 + 3x)^2 + 2(x^2 + 3x) - 8(x^2 + 3x) = 0

collecting and rearranging terms ___ (x^2 + 3x)^2 - 4(x^2 + 3x) + 4 = 0

factoring ___ [(x^2 + 3x) - 2][(x^2 + 3x) - 2] = 0

(x^2 + 3x - 2)^2 = 0

x^2 + 3x - 2 = 0

use quadratic formula to find solutions