I have one more question I need to ask about algebra, this one is a perform the indicated operation question.
4x 5x
----- - ----
x^2-9 x^2+4x-+3
I am really confused on the -+3 part, I don't know if my teacher made a typo or what, because without the - in that part it would be easily factorable.
oops it didn't write the question like i wanted it to, here I'll fix it
4x/x^2-9 - 5x/x^2+4x-+3
I also think the -+ is a typo error by your teacher. Assume it is +
Then you have
4x/[(x+3)(x-3)] - 5x/[(x+3)(x+1)]
= [1/(x+3)][4x(x+1)-5x(x-3)]/[(x+1)(x-3)]
= [1/(x+3)][-x^2+19x]/[(x+1)(x-3)]
= -x(x-19)/[(x+1)(x-3)(x+3)]
I don't guarantee I did that right. I created a common denominator, but it is still pretty messy.
To simplify the expression, we need to combine the fractions by finding a common denominator. In this case, the denominators are (x^2 - 9) and (x^2 + 4x - 3).
First, let's factor the denominators:
(x^2 - 9) = (x + 3)(x - 3)
(x^2 + 4x - 3) cannot be factored further.
Now we have:
4x/(x + 3)(x - 3) - 5x/(x^2 + 4x - 3)
To simplify the expression, we need to find a common denominator for these two fractions. The common denominator will be (x + 3)(x - 3)(x^2 + 4x - 3).
Multiplying the first fraction by (x^2 + 4x - 3)/(x^2 + 4x - 3) and the second fraction by (x - 3)/(x - 3), we have:
[4x(x^2 + 4x - 3)]/[(x + 3)(x - 3)(x^2 + 4x - 3)] - [5x(x - 3)]/[(x + 3)(x - 3)(x^2 + 4x - 3)]
Expanding the numerator of each fraction, we get:
[4x^3 + 16x^2 - 12x - 5x^2 + 15x]/[(x + 3)(x - 3)(x^2 + 4x - 3)]
Combining like terms in the numerator, we have:
[4x^3 + 11x^2 + 3x]/[(x + 3)(x - 3)(x^2 + 4x - 3)]
Finally, the expression is simplified to:
(4x^3 + 11x^2 + 3x)/[(x + 3)(x - 3)(x^2 + 4x - 3)]
Regarding the -+3 part of the denominator, it seems like there might be a typo or a mistake in the expression you provided. The correct expression should have a single term with an algebraic sign, such as -3 or +3, not -+3. Double-check the original problem or consult your teacher for clarification.