Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. If y = - 7 when x = - 2, and y = 5 when x = 1, express y in terms of x. Show your work.

Let a and b the two numbers. So y = a - b. one number varies directly as x, a = k1x. while the other number varies inversely as x, b = k2/x. so the equation y = k1x - k2/x

At y = - 7, x = 2 then - 7 = - 2k1 + k2/2

At y = 5, x = 1 then 5 = k1 - k2

Solving k1 and k2, 3 and - 2 respectively

So y = 3x+2/x