Is (1+x)/(x+1) =2 a Valid equation? | Maths Problems |

Added: 2026-05-09

[00:00:00]Hello everyone. Welcome to Rasa's classroom. Today we are solve a interesting math problem which is 1 + x over x + 1 is equal to 2.

[00:00:10]X is equal to what? Is it a valid equation?

[00:00:14]Please comment my video. And it's just for fun. Don't be serious. Which is 1 + x over x + 1 is equal to 2.

[00:00:22]So first of all, if you think 1 + x over x + 1 is equal to 2.

[00:00:30]Now this this cancel, it will be 1 is equal to 2.

[00:00:36]So 1 cannot be equal to So you can easily you can't solve this question like this method.

[00:00:45]So how to solve this interesting math question? It is not math, it's just for fun. Don't be serious.

[00:00:52]1 + x over x + 1 So this 1 + x I take here 1 + x.

[00:01:01]And this two times this, it will be two times x + 1.

[00:01:08]Now this is 1 + x and this two times x, this is 2x. Two times one, this is two.

[00:01:19]Now at this moment you can say here this 2x - x is it will be x and this 2 - 1 or 1 - 2, this is - 1.

[00:01:30]So we are find out here x is equal to -1.

[00:01:34]This is our answer.

[00:01:37]But if I use both side whole square you can try other method. So here which is 1 + x bracket power is two is equal to 2x + 2 bracket power is two.

[00:01:54]Now this is 1 + x * 1 + x.

[00:02:01]And this is 2x + 2 * 2x + 2.

[00:02:11]Now, at this moment you can say this 1 * 1 this is 1 + 1 * x this is x + x * 1 this is x.

[00:02:21]And x * x this is x to the power 2. And this is 2x * 2x it will be 4x to the power 2 + 2x * 2 this is 4x + 2 * 2x it will be 4x + 2 * 2 this is 4.

[00:02:39]Or you can use here is algebra formula which is a + b whole square a + b whole square which is a square + 2ab + b square.

[00:02:48]Then this is 4x square so I take 4x square this side it will be 4x to the power 2.

[00:02:55]Then this is 4x + 4x which is 8x I take this 8x here then plus this is 4 I take this 4 here is equal to this is x square.

[00:03:07]But this x + x this is 2x.

[00:03:11]This is addition and this is + 1.

[00:03:15]Now if I move on this below in this side it will be negative so this expression it will be 4x to the power 2 + 8x + 4 - x to the power 2 I just move on this below in this side it will be negative x - 1 is equal to 0.

[00:03:35]Now this is this minus this it will be 3x square.

[00:03:41]Then 8x and this x + x this is 2x so I take this two here this two here 8x - 2x this is 6x.

[00:03:56]And this is 4 - 1 this is 3.

[00:04:01]Is equal to 0.

[00:04:03]Now, if I divide both side by 3 which is x to the power 2 + 2x + 1 is equal to 0. Now, if I apply here this mass formula which is a square + 2ab + b square, so this is x + 1 bracket power is 2 is equal to 0.

[00:04:24]Now, which is x + 1 is equal to 0. Then, this is x is equal to -1. So, we are find out x is equal to -1. Let's verify.

[00:04:37]1 + x over x + 1 is equal to 2.

[00:04:45]Then, we are find out x is equal to -1.

[00:04:48]So, if I take this -1 here, x - 1 - 1 this is -1 + 1 is equal to 2. So, we are find out 0 is equal to 2. So, 0 cannot be equal to so you can say here no real solution no real no solution in this mass problem. No solution in this mass problem. It's just for fun.

[00:05:16]Don't be serious. Thank you all if you enjoy this mass problem. Please subscribe my channel others interesting video. Goodbye. Take care everyone.