Step-by-step explanation:

solution:

-a and its reciprocal is 1%2Fa. "is the same as" means "equals"

The additive inverse of a number (-a), divided by 12 (-a%2F12) is the same as (=) one less than (-1) three times its reciprocal (3%2A%281%2Fa%29=3%2Fa). Put it all together:

-a%2F12=%283%2Fa%29-1

Add 1 to both sides:

1-a%2F12=3%2Fa

LCD on the left is 12, so:

%2812-a%29%2F12=3%2Fa

Cross-multiply (numerator on the left times denominator on the right equals denominator on the left times numerator on the right)

a%2812-a%29=36

12a-a%5E2=36

-a%5E2%2B12a-36=0

Multiply by -1:

a%5E2-12a%2B36=0

Trinomial is a perfect square:

%28a-6%29%28a-6%29=0

Hence a=6

Check:

-%286%29%2F12=%283%2F6%29-1

-1%2F2=1%2F2-1=-1%2F2 Answer checks.

Answer:

x=6

Step-by-step explanation:

atq, let the no. be x

then -x/12=3/x-1

12-x/12=3/x

12x-x^2=36

x^2-12x+36=0

by splitting

x^2-6x-6x+36=0

x(x-6)-6(x-6)=0

(x-6)^2=0

x=6