what would be the answer to this question? The answer i got isn't one of the choices:
(x/x-3) - (x+1/x+3)
I got 1/x+3
What you typed does not make sense. Perhaps you mean:
[ x(x+3) - (x+1)(x-3)] / (x^2-9) ???
[ x^2 + 3x - x^2 +2 x + 3 ] /(x^2-9)
(5x+3)/(x^2-9)
probably meant:
x/(x-3) + (x+1)/(x+3)
and then Damon's steps take over
its x/(x-3) - (x+1)/(x+3)
How did you get that answer?
put it all over a common denominator.
How do you add
2/3 + 5/7 ?
You use the common denominator of 3*7. Do this the same way.
To simplify the expression (x/x-3) - (x+1/x+3), we need to find a common denominator for the two fractions.
The denominators in this case are x-3 and x+3. The lowest common denominator is the product of these two denominators. So, the common denominator would be (x-3) * (x+3).
To rewrite the fractions with the common denominator, we need to multiply the numerator and denominator of each fraction by the factor that is missing in each fraction.
For the first fraction, (x/x-3), the missing factor is x+3. So, we multiply the numerator and denominator by (x+3):
[(x * (x+3))/((x-3) * (x+3))]
For the second fraction, (x+1/x+3), the missing factor is x-3. So, we multiply the numerator and denominator by (x-3):
[((x + 1) * (x-3))/((x+3) * (x-3))]
Now, we can rewrite the expression as:
[(x * (x+3))/((x-3) * (x+3))] - [((x + 1) * (x-3))/((x+3) * (x-3))]
Simplifying further:
[(x^2 + 3x) - (x^2 - 2x - 3)]/((x-3) * (x+3))
Combining like terms, we get:
(5x + 3)/((x-3) * (x+3))
Therefore, the simplified expression is (5x + 3)/((x-3) * (x+3)).