Question

Simplify the rational expression. State any excluded values. x-2/x^2+3x-10

Simplify the rational expression. State any excluded values. 3x-6/x-2

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Answer 1

You'll need to factor any expressions that can be factored (denominator in the first one; numerator in the 2nd one). Then cancel any common factors.

Answer 2

"Excluded values" are any values that will make the den'r=0 (BEFORE you reduce to lowest form). You will see what those are, after you factor.

Answer 3

I'll do an example similar to your first one:

\[\Large \dfrac{ x-3 }{ x^2-x-6 }=\dfrac{ x-3 }{ (x-3)(x+2) }=\dfrac{ 1 }{ x+2 }\]

So excluded values are x=3 and x=-2. Fully simplified form is \(\Large \dfrac{ 1 }{ x+2 }\)

Answer 4

@DebbieG sorry i had some problems but i still didnt get what they need over here... i mean " State any excluded values"

Answer 5

can you solve that equation please @DebbieG

Answer 6

Can I solve what equation? I don't understand your question.

Again, the "excluded values" are those values for x that would make the denominator = 0, BEFORE you do any reducing to lowest terms. In my example above, once factored, you can see that if x=3 or x=-2, the den'r will be 0. So those values are excluded, they are not in the domain of the expression.

Answer 7

both of them @DebbieG

Answer 8

You don't have any "equations to solve", you just have expressions to be simplified. Unless you mean, solving the equation for the den'r=0, which is just a basic quadratic equation, and it factors, so you can apply the zero factor property:

\[\Large x^2-x-6 =0\]\[\Large (x-3)(x+2) =0\]\[\Large x-3=0 \text{ or } x+2=0\]\[\Large x=3 \text{ or } x=-2\]

Answer 9

I won't do your problems for you. I'm showing you exactly HOW to do your problems - you need to do them yourself or you won't learn the concept. Please ask questions, if there is something that I've done in my example problem that you don't understand, ask about it.

Answer 10

I think your 2nd problem is actually easier than your first, so maybe you should start there:
\[\Large \dfrac{ 3x-6 }{ x-2 }\]

Factor the numerator, and then IF you have any common factors, reduce. That's the "simplification" part.

For the "excluded values" part, look at the denominator (BEFORE simplifying) and exclude any values of x that make the den'r=0.

Answer 11

how can i know if there is common factors