Question #a71e9

3 Answers
Sep 19, 2016

Answer:

#x=color(green)(-10/3)#

Explanation:

Given
#color(white)("XXX")4/(x+2)+1/(x+3)=8/(x+2)#

Multiplying both sides by #(x+2)(x+3)#
#color(white)("XXX")4(x+3)+1(x+2)=8(x+3)#

Simplifying
#color(white)("XXX")5x+14=8x+24#

#color(white)("XXX")-3x=10#

#color(white)("XXX")x=-10/3 (=3 1/3)#

Sep 19, 2016

Answer:

#x=-10/3#

Explanation:

Basically we need to isolate #x# so I will first multiply both sides by #x+2#

#4+(x+2)/(x+3)=8#
now move #4# over
#(x+2)/(x+3)=4#
now multiply both sides by #x+3#
#x+2=4x+12#
Move like terms to each side
#-3x=10#
Solve for #x#
#x=-10/3#

As a final step always plug in and check your answer.

Sep 19, 2016

Answer:

#x=-10/3#
This solution is not the most efficient on purpose: The objective is to demonstrates a basic principle that may be used else ware.

Explanation:

Given:#" "4/(x+2)+1/(x+3)=8/(x+2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#[4/(x+2)color(red)(xx1)]+ [1/(x+3)color(blue)(xx1)]" "=" "[8/(x+2)color(green)(xx1)]#

#color(white)(.)#

#[4/(x+2)color(red)(xx(x+3)/(x+3))]+ [1/(x+3)color(blue)(xx(x+2)/(x+2))]=[8/(x+2)color(green)(xx(x+3)/(x+3))]#

#color(white)(.)#

#[(4(x+3))/((x+2)(x+3))] +[(x+2)/((x+2)(x+3))] =[(8(x+3))/((x+2)(x+3))] #
#color(white)(.)#

Multiply both sides by #(x+2)(x+3)# giving:

#4(x+3)" "+" "x+2" "=" "8(x+3)#

#color(white)(.)4x+12" "+" "x+2" "=" "8x+24#

#" "5x+14" "=" "8x+24#

#" "-10" "=" "3x#

#" "x=-10/3#