If a certain positive number is added to 8 times the reciprocal of 3 more than the number, the result is 6.
Change the words "a certain positive number" and "the number" both to x:
If x is added to 8 times the reciprocal of 3 more than x, the result is 6.
Change the words "3 more than x" to "x+3", since to get 3 more than x,
you put +3 after it:
If x is added to 8 times the reciprocal of x+3, the result is 6.
Change the words "the reciprocal of x+3" to .
If x is added to 8 times , the result is 6.
Change the words, "8 times to .
If x is added to , the result is 6.
Change the words "If x is added to " to "".
, the result is 6.
Change the words "the result is" to an equal sign .
.
Multiply through by the LCD, and solve the quadratic. It will factor.
You'll get two answers, one negative and the other positive. You
only want the positive one, since that's what the original problem
says.
Edwin