Solve for x: (x^2+x^2)/(x+1)^2=3

Expert Answers
justaguide eNotes educator| Certified Educator

The equation `(x^2+x^2)/(x+1)^2=3` has to be solved for x.

`(x^2+x^2)/(x+1)^2=3`

=> `(x^2+x^2) = 3*(x+1)^2`

=> `2x^2 = 3x^2 + 6x + 3`

=> `x^2 + 6x + 3 = 0`

`x1 = (-6 + sqrt(36 - 12))/2 = -3 + sqrt 6`

`x2 = -3 - sqrt 6`

The solution of the equation is `-3 + sqrt 6` and `-3 - sqrt 6`

elekzy | Student

first of all, to remove the fraction, multiply both sides by (x+1)^2

x^2+x^2=3(x+1)^2

simplify

 2x^2=3(x^2+2x+1)

2x^2=3x^2+6x+3

collect like terms

0=3x^2-2x^2+6x+3

0=x^2+6x+3

this cannot be simplified by factoring...so, its best to use the quadratic formula

 

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