 Hi, and how are you all today? The question says if 1 divided by 6 factorial plus 1 divided by 7 factorial is equal to x divided by 8 factorial Find x now in this question. We need to find x where 1 divided by 6 factorial plus 1 divided by 7 factorial is equal to x divided by 8 factorial also We know that n factorial is Equal to 1 multiplied by 2 multiplied by 3 multiplied by all the natural numbers till n Similarly, we have 8 factorial as 8 multiplied by 7 multiplied by 6 factorial 7 factorial as 7 multiplied by factorial now Substituting the values in the above mentioned Expression we have 1 divided by 6 factorial or 6 factorial plus 7 factorial as 7 multiplied by 6 factorial is equal to x divided by 8 multiplied by 7 multiplied by 6 factorial what we did over here We just substituted the value of 7 factorial which we found out 8 factorial which we found out in the given expression now taking 1 by 6 factorial common as Common multiple we have 1 by 6 factorial 1 plus 1 by 7 in the right inside Equal to 1 by 6 factorial we are left with x divided by 8 multiplied by 7 on Canceling out 1 by 6 factorial from both the sides we have 1 plus 1 by 7 is equal to x divided by 8 multiplied by 7 or we have On taking 7 as the LCM we have 7 plus 1 in the numerator is equal to x divided by 8 by 7 7 will get cancelled out with each other we left with 8 is equal to x by 8 which gives us the value of x as 64 8 multiplied by 8 so our answer is This completes our session. I hope now you know what a factorial notation is all about take care