Need Help so0o COnfused (math)?

Question

When The reciprocal of a positive number is added to the reciprocal of 12, the sum is the reciprocal of two less than the original number?What is the number?

I need step by step Process because i am So0o0o Confused

Answer 1

put the sentence into a mathematical "sentence"

1/n+1/12=1/(n-2)

let's mutliply both sides by 12n

12+n=12n/(n-2)

and then both sides by (n-2)

12n-24+n^2-2n=12n

so n^2-2n-24=0

(n-6)(n+4)=0

so n= minus 4 or 6

but we are told it's positive so we can discard the -4

the answer is 6

.

Answer 2

If you fall for "I can help u for that," you deserve to be scammed. Maybe he will also give you "free" tutoring in English.

Let the unknown number be x. The conditions state that 1/x + 1/12 = 1/(x - 2). Multiply through by 12x*(x - 2) to get 12*(x - 2) + x*(x - 2) = 12x. This simplifies to x^2 - 2x - 24 = 0, or (x - 6)(x + 4) = 0. The solutions are x = 6 or -4, but we are looking for a positive number, so the answer is 6.

Answer 3

ok so let x be the original number.
reciprocal of original is 1/x.
so the equation would be:

1/x + 1/12 = 1/(x - 2)

multiply by the least common denominator which is 12x(x-2) and u'll get:

12(x-2) + x(x-2) = 12x

12x - 24 + x^2 -2x = 12x

x^2 -2x -24 = 0

(x - 6)(x + 4) = 0

x = 6, -4

since you're looking for a positive number then the original number is 6.

Answer 4

n = number...

1/n + 1/12 = s

s= 1/ (n-2)

1/n + 1/12 = 1/(n-2)

Then you need to solve this by doing common denominators:

12(n-2) + n(n-2) = 12n

now solve for n:
12n - 24 + n^2 -2n = 12n
n^2 -10n - 12n - 24 =0
n^2 -2n -24 = 0

(n+4) (n-6) =0

n= 6,-4

the number is not negative because of the original stimulation in the question, so the number is 6...

Answer 5

n = positive number
n-2 = two less than the original number

1/n + 1/12 = 1/(n-2)

so n = 6.

Answer 6

I think what you mean is

(1/x) + (1/12) = (1/(x -2))

1 + x/12 = x/(x-2)

(x-2) + (x(x-2))/12 = x

12x - 24 + x^2 - x = x

12x -24 + x^2 -2x = 0

x^2 + 10x -24 = 0

(x + 12)(x - 2) = 0

x = -12, x = +2

x is a positive number (from question);

so x = 2

Answer 7

i don't know the answer but I know it can't be 2, because 1/(x - 2) would be undefined (division by zero)