Hi I am in need of help, please... The question says to perform the indicated operation.
x^2+2x-3/x^2-9 Divided By x^2-1/x^3-27
I put divided by in the middle to show that it is dividing two rational expressions.
Try simplifying
x^2+2x-3/x^2-9 to (x+3)(x-1)/[(x+3)(x-3)]
= (x-1)/(x-3)
Similarly factor what you can in the x^2-1/x^3-27
and you will get some more cancellations when you do the final division.
Hint: x^3-27 can be factored, and one of its factors is (x-3). I wil leave you to figure out the other one.
Ooo ok thanks so much, I got it :D
Sure, I'd be happy to help you with that math problem!
To divide two rational expressions like the one you mentioned, you first need to simplify each expression separately and then divide them. Let's start with the numerator and denominator of the left rational expression.
Numerator of the left expression:
The numerator of the left expression is x^2 + 2x - 3. It is already simplified, so we don't need to do anything to it.
Denominator of the left expression:
The denominator of the left expression is x^2 - 9. This can be factored as the difference of squares: (x - 3)(x + 3).
Now let's simplify the right rational expression.
Numerator of the right expression:
The numerator of the right expression is x^2 - 1. This is a difference of squares and can be factored as (x - 1)(x + 1).
Denominator of the right expression:
The denominator of the right expression is x^3 - 27. This is the difference of cubes and can be factored as (x - 3)(x^2 + 3x + 9).
Now that we have simplified both rational expressions, we can perform the division.
Dividing the two expressions:
To divide two rational expressions, we keep the first rational expression the same and multiply it by the reciprocal of the second rational expression. The reciprocal of a rational expression is obtained by flipping its numerator and denominator.
So the division can be written as:
(x^2 + 2x - 3) / (x^2 - 9) ÷ (x^2 - 1) / (x^3 - 27)
And this simplifies to:
(x^2 + 2x - 3) / (x^2 - 9) * (x^3 - 27) / (x^2 - 1)
To multiply these two rational expressions, we multiply the numerators together and the denominators together:
[(x^2 + 2x - 3) * (x^3 - 27)] / [(x^2 - 9) * (x^2 - 1)]
To simplify this final expression, we would need to distribute and combine like terms in both the numerator and denominator.
I hope this helps! Let me know if you have any further questions.