 Hello friends, welcome to the session. I am Alka and today we are going to find the roots of the following equations that is 1 upon x plus 4 minus 1 upon x minus 7 equal to 11 upon 30, where x is not equal to minus 4 and 7. Now, let's start with the solution. On taking LCM here, we see that x plus 4 and x minus 7 is the LCM. We get x minus 7 minus x plus 4 equal to 11 upon 30. This implies x minus 7 minus x minus 4 upon x square x square minus 3x minus 28 equal to 11 upon 30. Or we can say, xx cancel out minus 7 and minus 4 equal to minus 11 upon x square minus 3x minus 28 equal to 11 upon 30. Now, on cross multiplying, we get 11 into x square minus 3x minus 28 equal to minus 11 into 30. This implies 1111 cancel out. This implies x square minus 3x minus 28 equal to minus 30. This implies x square minus 3x minus 28 plus 30 equal to 0. This implies x square minus 3x plus 2 equal to 0. Now, this is our quadratic equation on comparing this equation with ax square plus bx plus c equal to 0. We have a equal to 1, v equal to minus 3 and c equal to 2. We can calculate the value of d which is b square minus 4ac. This implies d equal to minus 3 square minus 4 into 1 into 2. This implies d equal to 9 minus 8. Therefore, d equal to 1. Now, we can calculate the roots. Alpha equal to minus b plus square root of b upon 2a and beta equal to minus b minus square root of b upon 2a. Now, alpha equal to minus of minus 3 plus square root of 1 upon 2 into 1. This gives alpha equal to plus 3 plus 1 upon 2. This implies alpha equal to 2. Now, we will calculate the value of beta. Beta equal to minus v minus square root of b upon 2a. This gives minus of minus 3 minus square root of 1 upon 2 into 1. This implies plus 3 minus 1 upon 2. This implies beta equal to 2 upon 2 or beta equal to 1. Hence, the roots are 2 and 1. Hope you understood the solution and enjoyed the session. Goodbye and take care.