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

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

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

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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