 Hello and welcome to the session. The given question says solve for x and we have 2 into 2x minus 1 divided by x plus 3 minus 3 into x plus 3 divided by 2x minus 1 is equal to 5. We are given that x is not equal to minus 3 and x is not equal to half. Let's start with the solution. The given equation is 2 times of 2x minus 1 divided by x plus 3 minus 3 times of x plus 3 divided by 2x minus 1 is equal to 5. Let this be equation number 1. Now to solve this equation let us take the term in this bracket which is 2x minus 1 divided by x plus 3 is equal to y. So this implies the term in this bracket which is x plus 3 divided by 2x minus 1 which can be written as 1 divided by 2x minus 1 divided by x plus 3 is equal to 1 divided by y and here this holds only when x is not equal to minus 3 and this holds only when x is not equal to half. Since for x is equal to minus 3 y is not defined and x is equal to half 1 divided by y is not defined. Now let us substitute the values in these two brackets and thus 1 implies 2 times of y minus 3 times of 1 divided by y is equal to 5 or we have 2i square minus 3 is equal to 5y and this we get on taking LCM on the left hand side and then cross multiplying it or we have 2y square minus 5y minus 3 is equal to 0. Let this be equation number 2. Now we shall solve this equation number 2 to get the values of y and then we shall substitute the values of y and this equation and then get the values of x. So let us start. Now by splitting the middle term this equation can further be written as 2y square minus 6y plus y minus 3 is equal to 0 taking 2y common from the first two terms and one common from the last two terms this can further be written as 2y into y minus 3 plus 1 into y minus 3 is equal to 0 or we have now taking y minus 3 common we have y minus 3 into 2y plus 1 is equal to 0. Now as we know if the product of two numbers is equal to 0 then either a is equal to 0 or b is equal to 0. So from here we can say that either y minus 3 is equal to 0 or we have 2y plus 1 is equal to 0 which further implies that y is equal to 3 or y is equal to minus 1 by 2. So first we shall substitute y is equal to 3 and get the value of x. Now we had assumed that 2x minus 1 divided by x plus 3 is equal to y. So when y is equal to 3 we have 2x minus 1 divided by x plus 3 is equal to 3 or we have 2x minus 1 is equal to 3x plus 9 or minus x is equal to 10 or x is equal to minus 10. Now let us substitute the other value of y which is minus half in this equation to get the other value of x. So when y is equal to minus half we have x minus 1 divided by x plus 3 is equal to minus half which on cross multiplying can be written as 2 times of 2x minus 1 is equal to minus of x plus 3 or we have 4x minus 2 is equal to minus x minus 3 or 5x is equal to minus 1 or x is equal to minus 1 upon 5. Therefore x is equal to minus 10 and x is equal to minus 1 by 5. So the values of x are minus 10 and minus 1 by 5 which we get on solving the given equation. So this is our answer hope you have understood it bye and take care.