Verified answer

solve for x over the real numbers

x-(3(x-1)/x)=(x+1)/x

multiple both sides by x

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

expand out terms on left hand side

x^2-3x+3=x+1

subtract x+1 from both sides

x^2-4x+2

use quadratic formula

x=(4+ or -sqrt(-4^2-4*2))/2

x=(4+sqrt(8))/2 or (4-sqrt(8))/2

simplify radicals

x=(4+2*sqrt(2))/2 or (4-2*sqrt(2))/2

factor 2 from numerator

x=(2(2+sqrt(2)))/2 or (2(2-sqrt(2)))/2

cancel common terms

x=2+sqrt(2) or 2-sqrt(2)

10^[(x +1)(3x + 4)] - 2 * 10^[(x +1)(x + 2)] = 10^(1 - x - x^2) resolution; 10*(3X2+7X+4)-2*10(X2+3X+2)=10*(1-X-X2) 3X2+7X+4-2X2-6X-4=1-X-X2 X2+X=1-X-X2 X2+X2X+X+X=1 2X2+2X-1=0