Question

\[\sqrt{4x+5}-\sqrt{x-1}=3\] please help need step by step instruct

Answer 1

\[\sqrt{4x+5}/\sqrt{x-1}=3\]
is that the right equation

Answer 2

yes

Answer 3

clear the radical
\[\sqrt{4x^2-x-5}/x-1 = 3\]

Answer 4

\[2x \sqrt{-x-5}=3x-1\]

Answer 5

ill let you solve it from there

Answer 6

how did you get 4x^s-x-5

Answer 7

cause i multiplied 4x-5 by x-1

Answer 8

oook i can see that there r 2 possible answers one of them being 1 and the aquare root of 4 is 2 so do i use the quadratic formula or aquare root method

Answer 9

is it \[\sqrt{4x+5}/\sqrt{x-1}=3\] Or is it\[\sqrt{4x+5}-\sqrt{x-1}=3\] These are two very different kinds of problem.

Answer 10

If it is the first that is pretty easy.
square both sides getting
(4x+5)/(x-1)=9 cross multiply getting:
9x-9=4x+5
5x=14
x=14/5

Answer 11

if it the second then I need to think about it lol

Answer 12

O.K if it is the subtraction (the second one) here is the solution:
x+5 and x=1\[\sqrt{4*5 +5}-\sqrt{5-1}=\sqrt{25}-\sqrt{4}=5-2=3\]
\[\sqrt{4*1+5}-\sqrt{1-1}=\sqrt{9}-\sqrt{0}=3-0=3\]

Answer 13

If you want to see the steps (kind of wobbly) to obtain the solution, let me know below.

Answer 14

its the second one and the answer is one and 5 but how did they get the answer

Answer 15

O.K. I am back. Here are the steps that I took to solve this thing. There may be other ways to solve this.
I am having connection problems. Can't even get the equation bar to work. will try later

Answer 16

Here goes w/o editor.
I will try and write the equation again so we have it all in one spot.
(4x+5)^1/2 -(x-1)^1/2 = 3 sq rt (4x+5) - sq rt (x-1) = 3
Step 1. (4x+5)^1/2 = 3 + (x-1)^1/2 Adding sq rt (x-1) to both sides.
Step 2. Square both sides getting:
4x+5=9+6(x-1)^1/2 + x - 1 now combine and transpose to get
3x-3 = 6(x-1)^1/2 Divide thru by 3 getting
x-1=2(x-1)^1/2
Step 3. Square both sides getting
x^2-2x+1=4(x-1) combine and simplify getting
x^2-6x+5=0

Step 4. Factor getting:
(x-5)(x-1) = 0 or
x-5=0 giving x=5
x-1=0 giving x=1

Hope this helps.