Solve #((x+1)/(x+2))+((x+2)/(x+3))+7/2=2# ?

1 Answer
Sep 17, 2016

Answer:

#x~=-1.63841# or #~=-2.79016#

Explanation:

#((x+1)/(x+2))+((x+2)/(x+3))+7/2=2#

#((x+1)(x+3)+(x+2)^2)/((x+2)(x+3)) = -3/2#

#2(x+1)(x+3)+2(x+2)^2=-3(x+2)(x+3)#

#2(x^2+4x+3) + 2(x^2+4x+4) =-3(x^2+5x+6)#

#2x^2+8x+6 + 2x^2+8x+8= -3x^2-15x-18#

#7x^2+31x+32=0#

Using the quadratic formula:

#x=(-31+-sqrt(31^2-4*7*32))/(2*7)#

#x=(-31+-sqrt(65))/14#

#x~= (-31+-8.06226)/14#

#x~=-1.63841# or #-2.79016#