Math Problem? Please help if you can!?

Question

Hi, does anyone know how to solve this problem? I would really appreciate it because I'm not sure how to do it.

Simplify: 1 / ( √x - √(x+1)

this sign √ is a square root by the way.
A big thanks to anyone who can help!

Answer 1

1/(Sqrt[x] - Sqrt[x+1])?

1/(Sqrt[x]-Sqrt[x+1]) =

multiply top and bottom by (Sqrt[x] + Sqrt[x+1]) (on the top, this just gives you that...on the bottom, it gives you a difference of squares that simplifies beautifully)

(Sqrt[x] + Sqrt[x+1]) / ((Sqrt[x] + Sqrt[x+1]) (Sqrt[x] - Sqrt[x+1]))

and from there it's just simplifying things...

= (Sqrt[x] + Sqrt[x+1]) / (Sqrt[x]^2 - Sqrt[x+1]^2)
=(Sqrt[x] + Sqrt[x+1]) / (x-(x+1)) = -(Sqrt[x] + Sqrt[x+1])

i'm pretty sure that's as simplified as you're gonna get...

Answer 2

Solve,

1 / ( √x - √(x+1)

Multiply the top and bottom by the factor ( √x + √(x+1), note the change in the sign from "-" to "+".


[1/( √x - √(x+1))] [ √x + √(x+1)]/[ √x + √(x+1)]

= [ √x + √(x+1)] / [x - (x+1)]

= √x + √(x+1) or -[√x + √(x+1)]

Answer 3

Multiply top and bottom by (√x + √(x+1)) to get
(√x + √(x+1))/(x-(x+1) [remember (a-b)*(a+b) = a² - b²]
So this becomes
√x + √(x+1)/(-1) or -(√x + √(x+1))

HTH

Doug

Answer 4

The answer is 1.

Start off by squaring everything.
This leaves 1^2 / (x - (x+1))
Which gives 1 / 1 when simplified.

Answer 5

1 / (√x - √(x+1))
multiply top and bottom by (√x + √(x+1))
= (√x + √(x+1)) / (√x - √(x+1))(√x + √(x+1)) =
(√x - √(x+1)) / (x + (x+1) =
(√x - √(x+1)) / (2x+1)
final answer

Answer 6

* sqrt(x) + sqrt(x+1) on the top and bottom

get (sqrt(x) + sqrt(x+1))/ (x - x - 1) =

-sqrt(x) - sqrt(x+1)