(2x+5)/(sqrt(x^(2)+3x+1))

THe value of x which satisfy the equation (sqrt(5x^(2)-8x+3))-sqrt((5x^(2)-9x+4))=sqrt((2x^(2)-2x))-sqrt((2x^(2)-3x+1))

Find the first 5 terms,in ascending powers of x, in the expansion of (2+3x)/(sqrt(1-5x^(2)))

lim_(x rarr oo)((sqrt(x^(2)+5)-sqrt(x^(2)-3))/(sqrt(x^(2)+3)-sqrt(x^(2)+1)))

lim_(x rarr1)(sqrt(x^(2)+8)-sqrt(10-x^(2)))/(sqrt(x^(2)+3)-sqrt(5-x^(2)))=

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

Differentiate the following function : (i) (x^(2) - 5x + 6)(x-3) , (ii) (sqrt(x) + 1/(sqrt(x)))^(2) , (iii) (3x^(2) + 2x + 5)/(sqrt(x))

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

If (sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))=3 then x=1)sqrt((2)/(3)2)sqrt((1)/(3))3)sqrt((2)/(5))sqrt((3)/(5))

((sqrt(x))^((3)/(5))times(sqrt(x))^((2)/(5))+2sqrt(x))/(2(sqrt(x))^((2)/(3))times(sqrt(x))^((1)/(3))+sqrt(x))=