How to simplify?

Question

[2(y+1)^1/2 - y(y+1)^-1/2] / (y+1) = ?

Answer 1

To simplify the given expression in the simplest way put (y+1)^1/2 = A
such that (y+1) = A^2
and y=A^2 - 1
and (y+1)^-1/2=1/A

Then the expression becomes
[2A - (A^2-1)/A]/A^2
or [(2A^2-A^2+1)/A]/A^2
or [(A^2+1)/A]/A^2
or (A^2+1)/A^3
Put back A^2 = y+1 Such that A^3 = (Y+1)^3/2
you get (y+1+1)/(y+1)^3/2
or (y+2)/(y+1)^3/2

Answer 2

First, factor out the coefficients of the quantities, (2-y).
[(2-y)(y+1)^(-1/2)]/(y+1)

Now, separate the equation, for readability.

(2-y)/1 * [(y+1)^(-1/2)]/(y+1)

Simplify by subtracting the exponents of the quantity y+1.

(2-y)/1 * (y+1)^(-3/2)

Now, multiply together and invert the quantity (making it have a positive exponent) to obtain the simplified equation.

(2-y)/[(y+1)^(3/2)]

hope you will get it

Answer 3

First, factor out the coefficients of the quantities, (2-y).
[(2-y)(y+1)^(-1/2)]/(y+1)

Now, separate the equation, for readability.

(2-y)/1 * [(y+1)^(-1/2)]/(y+1)

Simplify by subtracting the exponents of the quantity y+1.

(2-y)/1 * (y+1)^(-3/2)

Now, multiply together and invert the quantity (making it have a positive exponent) to obtain the simplified equation.

(2-y)/[(y+1)^(3/2)]

Answer 4

Take a factor of (y+1)^(-1/2) out of the top to get:
[(y+1)^(-1/2) . (2(y+1) - y)] / (y+1)
= [(y+1)^(-1/2) . (y+2)] / (y+1)
= (y+2) / (y+1)^(3/2).

Answer 5

[2(y+1)^1/2 - y(y+1)^-1/2] / (y+1)
= [2√(y+1) - y / √(y+1)] / (y+1)

multiply statement by √(y+1) / √(y+1)

= [2*(y+1) - y] / [(y+1)√(y+1)]
= [2y + 2 - y] / [(y + 1)^(3 / 2)]
= (y + 2) / [(y + 1)^(3 / 2)]

I don't think it will get any better than that.