If 2 is added to both the numerator and denominator of a fraction its value becomes half. if two is subtracted from both the numerator and denominator of the same fraction its value becomes 1/3. what is the original fraction"

The original fraction is .

Step-by-step explanation:

Solution,

Let the fraction be''.

Where 'x' is the numerator and 'y' is the denominator.

Now according to question, if 2 is added to both the numerator and denominator the value of the fraction becomes 1/2.

So, framing the above sentence in equation form, we get;

On using cross multiplication method, we get;

Now according to question, if 2 is Subtracted to both the numerator and denominator the value of the fraction becomes 1/3.

So, framing the above sentence in equation form, we get;

On using cross multiplication method, we get;

Now Substituting the equation 1 in equation 1 we get;

Now Substituting the value of x in equation 1 we get;

Hence The original fraction is .

it would open into a square depending on the type of envelope i’m not sure about the second part

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.