Calculate dy/dt using the given information.

(x+y)/(x-y)= x^2 + y^2; dx/dt = 12, x = 1, y = 0

multipy both sides by (x-y)

x+y=x^3 -yx^2-xy^2-y^3 check that.

dx/dt+dy/dt= 3x^2 dx/dt-2yx dx/dt-x^2dy/dt-y^2dx/dt-3y^2 dy/dt

gather terms....

dx/dt(1-3x^2+2yx+3y^2)=dy/dt (-1-x^2-3y^2)

check that carefully, it is easy to make an error in sign.
solve for dy/dt

To calculate dy/dt using the given information, we will use implicit differentiation. Let's start by differentiating both sides of the given equation with respect to t.

First, differentiate the left side of the equation:
d/dt [(x+y)/(x-y)]

To do this, we can use the quotient rule, which states that the derivative of (u/v) is (v * du/dt - u * dv/dt) / v^2.

So, applying the quotient rule to our expression, we have:
[(x-y)*(d/dt(x+y)) - (x+y)*(d/dt(x-y))] / (x-y)^2

Next, differentiate the right side of the equation:
d/dt (x^2 + y^2)

To differentiate x^2 with respect to t, we can use the chain rule:
d/dt (x^2) = 2x * dx/dt

To differentiate y^2 with respect to t, we can use the chain rule again:
d/dt (y^2) = 2y * dy/dt

So, the right side of the equation becomes:
2x * dx/dt + 2y * dy/dt

Now, we can substitute the given values into the equation:
dx/dt = 12, x = 1, y = 0

Substituting these values, we get:
2(1) * 12 + 2(0) * dy/dt = [(1-0)*(d/dt(1+0)) - (1+0)*(d/dt(1-0))]/(1-0)^2

Simplifying this equation gives us:
24 + 0 = (1 * (d/dt(1)) - (1) * (d/dt(1)))/1

Further simplifying, we have:
24 = 0

Since the left side of the equation does not equal the right side, we have a contradiction. Therefore, there is no solution for dy/dt using the given information.