How do you solve #\frac { 2} { x + 4} + \frac { 3} { x - 4} = \frac { 24} { ( x + 4) ( x - 4) }#?

1 Answer
Mia
Nov 30, 2016

No solution

Explanation:

This equation includes sum of quotient ,the denominator should be different from zero .
#" "#
Domain:
#" "#
#x-4!=0rArrx!=4#
#" "#
#x+4!=rArrx!=-4#
#" "#
#x in RR - {4,-4}#
#" "#
#2/(x+4)+3/(x-4)=24/((x+4)(x-4))#
#" "#
#rArr(2(x-4)+3(x+4))/((x+4)(x-4))=24/((x+4)(x-4))#
#" "#
#rArr(2x-8+3x+12)/((x+4)(x-4))=24/((x+4)(x-4))#
#" "#
#rArr(5x+4)/((x+4)(x-4))=24/((x-4)(x+4))#
#" "#
Therefore,
#" "#
#rArr5x+4=24#
#" "#
#rArr5x=24-4#
#" "#
#rArr5x=20#
#" "#
#rArrx=20/5#
#" "#
#rArrx=4#rejected
#" "#
Hence, no solution .

Related questions
Impact of this question
713 views around the world
You can reuse this answer
Creative Commons License