I really don't understand how you find or identify the restrictions at all for rational expressions, can someone talk me through it? I have a math exam Monday and I'm stressed. Thanks.

Here are some examples for my textbook if needed...

1) 2x + 1 / 2x - 1
2) x-5 / x^2 + 3x + 2
3) 3x + 1 / 2x^2 + 5x + 2

the only restrictions are because you cannot divide by zero. So, check the denominator of any rational expression. Wherever it is zero, those values must be omitted from the domain. Otherwise, all real numbers are allowed.

So, for #3 above, since
2x^2+5x+2 = (2x+1)(x+2)
the values x = -1/2 and -2 are not in the domain -- they would make the denominator zero. All other real values are allowed.

I understand that finding restrictions for rational expressions can be challenging. Let me guide you through the process step by step.

To find the restrictions for a rational expression, we need to identify the values of the variable that would make the denominator equal to zero. This is because division by zero is undefined in mathematics. Any value that makes the denominator zero must be excluded from the domain of the rational expression.

Now, let's apply this concept to the examples you've provided:

1) For the rational expression 2x + 1 / 2x - 1, we should set the denominator, 2x - 1, equal to zero and solve for x:

2x - 1 = 0
2x = 1
x = 1/2

Therefore, the expression is undefined when x = 1/2. This means that the restriction for this expression is x ≠ 1/2.

2) For the rational expression x-5 / x^2 + 3x + 2, we need to find the values of x that make the denominator, x^2 + 3x + 2, equal to zero. We can factorize the denominator to determine its roots:

x^2 + 3x + 2 = 0
(x + 2)(x + 1) = 0

From this, we obtain two possible values for x: -2 and -1. Therefore, the expression is undefined when x = -2 or x = -1. The restrictions for this expression are x ≠ -2 and x ≠ -1.

3) For the rational expression 3x + 1 / 2x^2 + 5x + 2, we should find the x-values that make the denominator, 2x^2 + 5x + 2, equal to zero. Again, we can factorize the denominator:

2x^2 + 5x + 2 = 0
(2x + 1)(x + 2) = 0

This time, we find two possible solutions for x: -1/2 and -2. Therefore, the expression is undefined when x = -1/2 or x = -2. The restrictions for this expression are x ≠ -1/2 and x ≠ -2.

Remember, when identifying restrictions, we are looking for the values that would make the denominator zero. Once we find these values, we determine that they are not allowed in the domain of the rational expression.

I hope this explanation helps you understand how to find the restrictions for rational expressions. If you have any further questions or need more examples, please let me know. Good luck on your math exam!