A Nice Algebra Problem | Math Olympiad | Find all roots?

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Find the value of x?
How to solve (x+2)(x+3)(x+4)(x+5) / (x-2)(x-3)(x-4)(x-5) = 1

In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem (x+2)(x+3)(x+4)(x+5) / (x-2)(x-3)(x-4)(x-5) = 1 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[brianwade]

Brute force was much quicker than all the substitution maneuvers you did. I just multiplied the numerator and denominator completely out. I got (x^4 + 14x^3 + 71x^2 + 154x + 120) / (x^4 - 14x^3 + 71x^2 - 154x + 120) = 1. Then I cross-multiplied and cancelled a whole lot of stuff. I got 28x^3 + 308x = 0. Thus x=0 is a root. Then I divided through by 28x and got x^2 + 11 = 0. Thus the other two roots are +-sqrt(11)i.

[فیروزاهنگری]

let. x^2+10=A

14Ax+14x=-14Ax-14x
Ax+x=0, x(A+1)=0
x=0. or A=-1
A=-1 then x^2+10=-1 , x=+-√11*i

[Nekodemus]

Don't get it, I've found x(x²+11)=0... cause first