How do you solve # 5/(x+1) - 1/2 = 2/3x + 3#?

1 Answer
Nov 10, 2017

Answer:

#x=1/8(-25+sqrt385)# or #x=1/8(-25-sqrt385)#

Explanation:

We will first write each side as a single fraction; then multiply this out and solve the quadratic equation that follows.

#5/(x+1)-1/2=(2x)/3+3#
#10/(2(x+1))-(x+1)/(2(x+1))=(2x)/3+9/3#
#(11-x)/(2x+2)=(2x+9)/3#

Here we cross-multiply, to get:

#3(11-x)=(2x+2)(2x+9)#
#33-3x=4x^2+22x+18#
#4x^2+25x-15=0#

You can now use The Formula or complete the square; I'd recommend The Formula.

#x=(-25+-sqrt(25^2-4xx4xx(-15)))/(2xx4)#

#x=(-25+-sqrt(625-240))/8#
#x=(-25+-sqrt385)/8#

#:. x=1/8(-25+sqrt385)# or #x=1/8(-25-sqrt385)#
#(x~~-0.672, x~~-5.58#)