Hi. I am starting a new section in Algebra, and I thought I understood it. But when I went to the back of my book to check the answers, they were way off. We are dividing and simplifying radical expressions and equations.

Hi there! I'd be happy to help you with dividing and simplifying radical expressions and equations in Algebra. Let's start by breaking down the process step by step.

When dividing radical expressions, it's important to simplify any radicals involved before performing the division. Here's a general approach to follow:

Step 1: Identify if there are any perfect square factors inside the radicals.
- For example, if you have the expression √(36), you would simplify it as 6 since 36 is a perfect square.

Step 2: Simplify the radicals by multiplying the numbers outside the radicals.
- For example, if you have the expression 4√(3), you would simplify it as 12√(3) since 4 * √(3) = 12√(3).

Step 3: Apply the division rules of radicals to simplify the expression as much as possible.
- For example, if you have the expression √(16) / √(4), you can simplify it as √(4), which is 2.

Now let's move on to simplifying radical equations. Here's a step-by-step process for simplifying and solving radical equations:

Step 1: Isolate the radical expression on one side of the equation.
- For example, if you have the equation √(x+5) = 7, isolate the radical expression by subtracting 5 from both sides to get √(x+5) - 5 = 7 - 5.

Step 2: Square both sides of the equation to eliminate the radical.
- Continuing from the previous example, squaring both sides gives ( √(x+5) - 5 )^2 = 2^2.

Step 3: Simplify the equation and solve for the variable.
- Expanding the squared expression on the left side of the equation, we get (x+5) - 10√(x+5) + 25 = 4.
- Rearrange the equation and combine like terms: x - 10√(x+5) + 20 = 0.
- Solve for x by isolating the radical term and then squaring both sides again if necessary.

Remember to always check your solutions in the original equation to ensure they satisfy the given conditions.

If you encounter any specific problems or need further clarification, feel free to provide an example, and I'll be happy to guide you through the steps.

I don't know what to do, except pray for you.

If you have specific questions, ask.

ARe there example problems in the text?

Bobpursley is right -- you must ask specific questions in order to get help. We have no access to your text or your assignments.

So please post specific questions and let the teachers know what you understand about each one so far.