0 votes 0 votes 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 mehul vaidya asked Jan 16, 2019 mehul vaidya 248 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Verma Ashish commented Jan 16, 2019 reply Follow Share We already know that $(PQ)^*P=P(QP)^*$ so take RHS $x^* (yx^*)^* y=x^* y(x^* y)^*$ $=(x^*y)^+= LHS$ 1 votes 1 votes mehul vaidya commented Jan 16, 2019 reply Follow Share what is P & Q in this ? Please help 0 votes 0 votes Verma Ashish commented Jan 16, 2019 reply Follow Share In $x^* (\color {green} y \color{red}{ x^*})^* \color{green} y$ P is y and Q is $x$* then it becomes $x^* (P Q)^* P= x^* P(QP)^*= x^* y(x^* y)^*$ 1 votes 1 votes mehul vaidya commented Jan 19, 2019 reply Follow Share Thank you @Verma Ashish 0 votes 0 votes Please log in or register to add a comment.