How can i simplify my equation

Is ther anyway to simplify equation uo=-C/r , i want to explain uo with r not x and y

syms u uo ur v  Q C x y r 
u=C*y/(x^2+y^2)
v=-C*x/(x^2+y^2)
r=(x^2+y^2)^0.5
Q=atan(y/x)

ur=u*cos(Q)+v*sin(Q)
uo=-u*sin(Q)+v*cos(Q)
simplify(uo)

Answer 1

[Walter Roberson]

No, there isn't a way to simplify uo = -C/r, because it is not true.

If you substitute x = -7, y = 3 you will find that uo = C/r rather than -C/r

If you substitute x = 7, y = 3, you will find that uo = -C/r

The actual formula is that uo = -C * sign(x) / r

[esat gulhan]

It is true becase

r^2=x^2+y^2

uo=-C/(x*(y^2/x^2 + 1)^(1/2))

uo=-C/(x*((x^2+y^2)/x^2)^(1/2))

uo=-C/(x*((r^2)/x^2)^(1/2))

uo=-C/(x*((r/x))

uo=-C/(r)

when i substitute x = -7, y = 3 I find -0.131*C not -C/r

[Walter Roberson]

uo=-C/(x*((r^2)/x^2)^(1/2))
uo=-C/(x*((r/x))

The second of those two steps is fault. When x is negative, sqrt(x^2) is not x, it is -x . sqrt(x^2) is abs(x) for real-valued x. And abs(x)/x is not 1: it is sign(x)