What is x if 2/(2x-2) + 2/(2x+2) = 10

First, We'll factorize by 2 the denominators from the
given expression:

2/2(x-1) + 2/2(x+1) =
10

We'll simplify and we'll
get:

1/(x-1) + 1/(x+1) =
10

we'll move all terms to one
side:

1/(x-1) + 1/(x+1) - 10 =
0

Now, we'll determine the least common
denominator:

LCD =
(x-1)(x+1)

We notice that the result of the product is the
difference of squares:

(x-1)(x+1)  = x^2 -
1

We'll re-write the
equation:

x + 1 + x - 1 - 10(x^2 - 1) =
0

We'll remove the brackets and we'll combine and eliminate
like terms:

2x - 10x^2 + 10 =
0

We'll divide by -2 and we'll re-arrange the
terms:

5x^2 - x - 5 = 0

We'll
apply the quadratic formula:

x1 = [1 + sqrt(1 +
100)]/10

x1 =
(1+sqrt101)/10

x2 =
(1-sqrt101)/10

Since the roots are different
from the values 1 and -1, we'll consider as being valid.