Step 1 is to isolate one square root: =

Step 2, square both sides to get: =

I still have a square root after squaring, Remember !,

which I leave on the right side and take everything else to the left:

=

Caution: the left side is a big "mess" in the above step.

Squaring again: =

So, the only possible root is . It is a(n) root. (Fill in the second blank with REAL or EXTRANEOUS)

next Problem

(1 pt) Solve the equation: x+1/x-1=-6/x+3 + 8/x^2+2x-3

First to clear denominators, multiply both sides by and cancel denominators:

Then get everything to left side: = 0.

Simplify, factor and check solutions:

Last problem:

(1 pt) You drop a rock into a deep well. You can't see the rock's impact at the bottom, but you hear it after 7 seconds. The depth of the well is _________ feet. Ignore air resistance. The time that passes after you drop the rock has two components: the time it takes the rock to reach the bottom of the well, and the time that it takes the sound of the impact to travel back to you. Assume the speed of sound is 1100 feet per second.

Note: After seconds the rock has reached a depth of "d" feet where

Set up and solve a quadratic equation: d=16t^2