Need to know what to do...?

let the number be n

reciprocal of n = 1/n

6 less than n = n-6

therefore we have:

(1/n) + [1/(n-6)] = 7/n

6/n = 1/(n-6)

6(n-6) = n

6n-36 = n

5n = 36

n = 36/5

Well, let's see.

Let n be the number

then

the number plus its reciprocal is 6 less than 7 times its reciprocal:( is that what the words mean?)

n+1/n = 7*(1/n)-6

mult by n:

n^2+1 = 7 -6n

n^2+6n-6=0

Doesn't seem like I translated the statement correctly. Is that a verbatem wording?

1/x+1/(x-6)=7/x

6/x=1/(x-6)

cross multiplying

6(x-6)=x

6x-36=x

5x=36

x=36/5

check 5/36+5/6=5+30/36=35/36

checks

1/x + 1/(x-6) = 7*(1/x)

1/x + 1/(x-6) = 7/x

(x-6)/(x(x-6)) + x/(x(x-6)) = 7/x

(2x-6) / (x^2-6x) = 7/x

2x-6 = (7x^2 -42x) /x

2x-6 = 7x - 42

5x = 36

x = 36/5