 Hello and welcome to the session. Let's work out the following problem. It's a solve for x. So let's now move on to the solution the given equation is 4x minus 3 upon 2x plus 1 minus 10 into 2x plus 1 upon 4x minus 3 is equal to 0 where x is given to be not equal to minus 1 by 2 and it is not equal to 3 by 4 now We see that the This expression is the reciprocal of this so let 4x minus 3 upon 2x plus 1 is equal to y So this implies 2x plus 1 upon 4x minus 3 is equal to 1 upon y Now the given equation becomes y minus 10 into 1 by y is equal to 3 now taking LCM LCM would be y and Here we have y square minus 10 is equal to 3 Now this implies y square minus 10 is equal to 3 y Now this implies y square minus 3 y minus 10 is equal to 0 This implies y square Minus 5 y plus 2 y Minus 10 is equal to 0 Now taking y common from the first two terms we have y into y minus 5 Taking two common from the last two terms we have 2 into y minus 5 is Equal to 0 now taking y minus 5 common we have y minus 5 into y plus 2 is equal to 0 Now this implies y minus 5 is equal to 0 or y plus 2 is equal to 0 So this implies y is equal to 5 or Y is equal to minus 2 now y is 4x minus 3 upon 2x plus 1 and This is equal to 5 and here 4x minus 3 upon 2x plus 1 is equal to minus 2 Now we'll simplify this so we have 4x minus 3 is Equal to 5 into 2x plus 1 cross multiplying now again. We have 4x minus 3 is equal to 10 x plus 5 So this implies 4x minus 10x is equal to 5 plus 3 So this implies minus 6x is equal to 8 So this implies x is equal to 8 by minus 6 and this implies x is equal to Minus 4 by 3 Now we'll solve this so we have 4x minus 3 is equal to minus 2 into 2x plus 1 4x minus 3 is equal to minus 2 into 2x is minus 4x minus 2 So this implies 4x plus 4x transposing minus 4x to the left hand side It becomes plus 4x minus 2 plus 3 So we have 4x plus 4x is 8x is equal to 1 So this implies x is equal to 1 upon 8 So the solution of the given equation is x is equal to minus 4 by 3 or x is equal to 1 upon 8 So this completes the question do take care of your calculations Why and take care?