Question

when the reciprocal of the number x and x+2 are added together, the sum is 5/12, find the numbers

Answer 1

Given numbers=x &x+2
The reciprocal of this number=1/x &1/x+2
sum of this reciprocal=5/12
so,a/c to questions......
1/x+1/x+2=5/12...

x+2+x/x(x+2)=5/12
2x+2/x2+2x=5/12
24x+24=5x2+10x=(after cross multiplying).
5x2+10x-24x-24
5x2-14x-24=0
5x2-20x+6x-24=0
5x(x-4)+6(x-4)=0
(5x+6)(x-4)=0
x=4, x=-6/5...
But...
number is cannot in negative and fraction...
Then the numbers is 4,& 6...
I hope that i help u and u can understand it very simply.....
@akash kumar...

Answer 2

1/x + 1/x+2 = 5/12
x+2+x/x^2+2x = 5/12
12(2x+2) = 5(x^2+2x(
24x+24 = 5x^2+10x
=5x^2-14x-24
=5x^2-20x+6x-24
=5x(x-4)+6(x-4)
=(5x+6) (x-4)

(x=4)