`|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|`

det [[x + 4,2x, 2x2x, x + 4,2x2x, 2x, x + 4]]

By using properties of determinants,prove the following ,2xdet[[x+4,2x,2x2x,x+4,2x2x,2x,x+4]]=(5x+4)(4-x)^(2)

2x^2(x^3-x)-3x(x^4+2x)-2(x^2-3x^4)

(3x + 2x^2 + 4x^3) / (x-4)

Observe the following pattern (1x2)+(2x3)=(2x3x4)/(3)(1x2)+(2x3)+(3x4)=(3x4x5)/(3)(1x2)+(2x3)+(3x4)+(4x5)=(4x5x6)/(3) and find the of (1x2)+(2x3)+(3x4)+(4x5)+(5x6)

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(x)?

Find the range of the following function f(x)=(x^(4)-x^(2)-2x+8)/(x^(4)-x^(2)-2x+4)

Solve for x when (x+2)/(x-2)+(x-4)/(x+4)=6;(x!=2,-4)