<PRE><B>Question 132598</B>
Let x=the certain positive number

10 less than this number is x-10
The reciprocal of 10 less than the number is 1/(x-10)
4 times the reciprocal is 4/(x-10)

Now we are told the following:

x + 4/(x-10)=5  multiply each term by (x-10)
x(x-10)+4=5(x-10)  get rid of parens

x^2-10x+4=5x-50  subtract 5x from and add 50 to both sides

x^2-10x-5x+4+50=5x-5x-50+50  collect like terms

x^2-15x+54=0   quadratic in standard form and it can be factored:

(x-6)(x-9)=0

x-6=0
x=6-----------------------possible solution
x-9=0
x=9---------------------------another possible solution

CK
for x=6
6+4/(6-10)=5
6-1=5
5=5-----------------------------x=6 is a solution
for x=9
6+4/(9-10)=5
6-4=5
2=5------------------------------x=9 is not a solution



Hope this helps---ptaylor</PRE>