How do you simplify: x/x^2 - 9 subtracted by x/x + 3 then adding 3/ x - 3. I got common denominators than simplified. I ended with -x^2 + x + 9. Where did I go wrong?
what you got aginst standard math notation?
x/(x^2-9) - x/(x+3) + 3/(x-3)
once you get the common denominator of (x^2-9), the numerator is
x - x(x-3) + 3(x+3)
= x-x^2+3x+3x+9
= -x^2+7x+9
so the final fraction can be written as
-(x^2-7x-9)/(x^2-9)
x/(x^2 - 9) - x/(x + 3) + 3/(x - 3)
The common denominator is (x^2 - 9).
Note that x^2 - 9 = (x + 3)(x - 3). Rewriting,
= x/(x^2 - 9) - x(x - 3)/(x^2 - 9) + 3(x + 3)/(x^2 - 9)
Combine all the terms in the numerator,
= ( x - x(x - 3) + 3(x + 3) ) / (x^2 - 9)
= (x - x^2 + 3x + 3x + 9) / (x^2 - 9)
= (-x^2 + 7x + 9) / (x^2 - 9)
Hope this helps~ `u`
To simplify the expression
(x / x^2 - 9) - (x / x + 3) + (3 / x - 3),
you correctly identified that you need to find the common denominators before combining the fractions. However, there seems to be an error in your simplification.
Let's go through the steps again to determine where the mistake occurred.
First, let's find the common denominators for the fractions: x^2 - 9 and x - 3.
The expression becomes:
x / (x + 3)(x - 3) - x^2 / (x^2 - 9) + (3 / (x - 3)).
Next, simplify each fraction by multiplying the numerator and denominator to get rid of any common factors:
x / (x + 3)(x - 3) - (x^2 / (x^2 - 3)(x + 3)) + (3 / (x - 3)).
Now, let's multiply out the denominators:
x / (x^2 - 9) - (x^2 / (x^2 - 9)) + (3 / (x - 3)).
To combine the fractions, we need to have the same denominator. In this case, the denominator is (x^2 - 9), which can be factored further as (x + 3)(x - 3).
Combining the fractions gives us:
(x(x - 3) - x^2 + 3(x + 3)) / (x + 3)(x - 3).
Simplifying the numerator gives:
(x^2 - 3x - x^2 + 3x + 9) / (x + 3)(x - 3).
This simplifies to:
(9) / (x + 3)(x - 3).
Therefore, the correct simplified expression is 9 / (x + 3)(x - 3). The error in your previous calculation could have been caused by a mistake during the combination of terms or a miscalculation. Double-check your steps to identify the discrepancy.