(x-1)/(x+2)+(x-3)/(x-4)=(10)/(3),quad n!=-2

Solve for x:(x-1)/(x+2)+(x-3)/(x-4)=(10)/(3),x!=-2,4

Solve for x : (x-1)/(x+2)+(x-3)/(x-4)=(10)/3,\ \ x!=-2,\ 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)

The value of lim_(x rarr oo)(2x^((1)/(2))+3x^((1)/(3))+4x^((1)/(4))+......+nx^((1)/(n)))/((2x-3)^((1)/(2))+(2x-3)^((1)/(3))+......+(2x-3)^((1)/(n))) is equal to

((4x-3) / (2x + 1))-10 ((2x + 1) / (4x-3)) = 3, x! =-1/2, 3/4

Coefficient of x^((n^2+n-14)/2) in, (x-1)(x^2-2)(x^3-3)(x^4- 4).........(x^n-n),(n>=8) is

Coefficient of x(n^(2)+n-14)/(2) in,(x-1)(x^(2)-2)(x^(3)-3)(x^(4)-4)......(x^(n)-n),(n>=8) is

" If (3x^(3)-8x^(2)+10)/((x-1)^(4))=(3)/(x-1)+(1)/((x-1)^(2))-(7)/((x-1)^(3))+(k)/((x-1)^(2)) then "k=

(lim)_(xvecoo)(2. x^(1//2)+3. x^(1//3)+4. x^(1//4)++ndotx^(1//n))/((3x-4)^(1//2)+(3x-4)^(1-3)+(3x-4^)^(1//3)++(3x-4)^(1//n)) (here n in N ,ngeq2 ) is equal to 1 dot2/(sqrt(3)) 2. (sqrt(3))/2 3. 1/2 4. 1/(sqrt(3)) 5. 2

Find the sum to n terms of the following series: (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+(x^(4)+(1)/(x^(4)))^(2)+