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 .
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Domain:
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#x-4!=0rArrx!=4#
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#x+4!=rArrx!=-4#
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#x in RR - {4,-4}#
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#2/(x+4)+3/(x-4)=24/((x+4)(x-4))#
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#rArr(2(x-4)+3(x+4))/((x+4)(x-4))=24/((x+4)(x-4))#
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#rArr(2x-8+3x+12)/((x+4)(x-4))=24/((x+4)(x-4))#
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#rArr(5x+4)/((x+4)(x-4))=24/((x-4)(x+4))#
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Therefore,
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#rArr5x+4=24#
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#rArr5x=24-4#
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#rArr5x=20#
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#rArrx=20/5#
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#rArrx=4#rejected
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Hence, no solution .

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