Doubt in Regular expression

Question

how to prove 

$(x^{*}y)^{*}x^{*}y = x^{*}(yx^{*})^{*}y$

I have already checked https://gateoverflow.in/290653/me_test_series?show=290690

It contains extra y.

x*y(yx*)*y

and I am not able to solve this , please help

Comments

We already know that $(PQ)^*P=P(QP)^*$

so take RHS  $x^* (yx^*)^* y=x^* y(x^* y)^*$

$=(x^*y)^+= LHS$

---

what is P & Q in     this ? Please help

---

In $x^* (\color {green} y \color{red}{ x^*})^* \color{green} y$

P is y and Q is $x$*  then it becomes $x^* (P Q)^* P= x^* P(QP)^*= x^* y(x^* y)^*$

---

Thank you @Verma Ashish