 Hello friends welcome to another problem solving session I hope these video sessions are useful to you please go through these sessions again and again till you understand and you can always post a query in the comment section okay so in this question it's been given that x plus 3 upon x minus 2 minus 1 of minus x upon x is 17 by 4 now by no means it looks like a quadratic equation but it can be reduced to one quadratic equation right it is not a quadratic equation in this form why because the degree is not to first of all it's not a polynomial itself so hence you know there is a degree is not defined here so hence we can't say or we can't you know categorize it in in in the category of quadratic equations at all but then it can be transformed into one how let us do that so if you see we can take LCM of the denominators x minus 2 and x so what is the LCM simply multiply them and that's the LCM is it now okay so hence it should not be called as LCM but this is the process so what you need to do is you need to multiply the denominators and basically make the denominator common so I'm making the denominator common so once I did that now it's left over what is the leftover process so hence x plus 3 will definitely be there but since you have you know there is an extra x here so you have to multiply it with x over there as well so this is how it is done now in the second case 1 minus x will definitely be there and that too with minus sign but it has to be it is with denominator x but there is an extra x minus 2 here so you multiply with x minus 2 to balance it this is how it is done and now it is 70 17 upon 4 now what to do simplify so the LHS will be x square plus 3x open the brackets and then here it will be nothing but minus so minus 1 minus x can be written as plus x minus 1 minus 1 minus x can be written as plus x minus 1 x minus 2 for avoiding errors I have done this and this is nothing but x square minus 2x isn't it and this is 17 upon 4 now what move ahead it is nothing but x square plus 3x plus now open the brackets there you'll get x square minus 2x minus x plus 2 right and this divided by x square minus 2x and this is equal to 17 upon 4 right now next what simplify again so club all the like terms x square plus x square is 2x square plus 3x minus 2x minus 2x goes so this disappears now x square 2x square plus 2 divided by x square minus 2x this is equal to 17 upon 4 now perform cross multiplication you will get 4 times 2x square plus 2 is equal to 17 times x square minus 2x right so this implies what is it this is 8x squared plus 8 this is equal to 17x squared minus 34x and if you simplify it further you will get the quadratic equation 17x square minus 8x square is 9x square minus 34x plus 8 equals 0 okay plus 8 is 0 so now again what do you need to do you can split the middle term so hence if you see 9 and 8 multiply these two you will get 72 right and minus 34 has to be broken down into B1 and B2 such that B1 B2 is 72 so what would how to do factorize this this is nothing but 2 into 36 in the first step itself it is pretty obvious that you know B1 could be minus 2 and B2 could be minus 36 so that I'm sorry it should be plus 36 no then I'm sorry this will be not minus 8 here it is it will be minus this will be minus 8 right small error in my calculation so it is minus a 17x square minus 34x minus 8 equals to 0 so now it becomes easier for me so B1 is 2 and B2 is minus 36 okay so how to go about it B1 B2 in this case is minus 7 yeah so now how to go about it so it is nothing but 9x square minus 34x can be written as minus plus 2x minus 36x minus 8 equals 0 is it it spreading the middle term so hence now what do you do take x common so hence it is 9x plus 2 and this is again you can write 9x plus 2 directly and what should I multiply here to get 30 minus 36x so you know this is 4 right so hence what are the factors 9x plus 2 and x minus 4 and this all equals 0 so hence what do we learn either 9x plus 2 is 0 or x minus 4 is 0 so your x is equal to minus 2 upon 9 or x equals 4 see how simple it is so the equation was not appearing to be a quadratic equation but then we transform it to into a quadratic equation then solve it by factorization method and we saw the solution to be x equals to minus 2 by 9 and x equals to 4 this is the solution so hence what is the learning if you if you see ratio of two linear terms and they are added together or subtracted together so there are a ratio of two linear terms isn't it and they are subtracted here then make rest assured it is going to lead to your quadratic equation that's what we just saw here okay so this is how you solve a equation which is not appearing to be quadratic in the very first glimpse