x-21/(x^2-9) - x/(3-x)
so I did x-21/((x-3)(x+3)) - x/-(x-3)
x-21+x(x+3)/((x-3)(x+3))
x-21+x^2+3x/((x-3)(x+3))
4x-21+x^2/((x-3)(x+3))
x^2+4x-21/((x-3)(x+3))
x(x+7)-3(x+7)/((x-3)(x+3))
(x+7)(x-3)/((x-3)(x+3)) the x-3 cancel out
so the answer is x+7/x+3 is this correct? Thank you
If you include the following brackets, you are correct.
I will cut-and-paste your answer , and put in the necessary brackets
(x-21)/(x^2-9) - x/(3-x)
so I did (x-21)/((x-3)(x+3)) - x/-(x-3)
= (x-21+x(x+3) )/((x-3)(x+3))
= (x-21+x^2+3x)/((x-3)(x+3))
4x-21+x^2/((x-3)(x+3))
= (x^2+4x-21)/((x-3)(x+3))
= ( x(x+7)-3(x+7) )/((x-3)(x+3))
= (x+7)(x-3)/((x-3)(x+3)) the x-3 cancel out
= (x+7)/(x+3) , x ≠ 3
Your answer is correct, have you learned about restrictions?
You answer is correct.
sorry, no we did not learn restrictions.
Thank you for checking my work.
To simplify the expression (x-21)/(x^2-9) - x/(3-x), you made several steps correctly until the last step. Let's go through it again and find the correct answer:
1. Factor the denominators:
(x^2-9) = (x-3)(x+3)
(3-x) = -(x-3)
2. Rewrite the expression:
(x-21)/((x-3)(x+3)) - x/-(x-3)
3. Add the fractions:
[x(x-21) - (-x)(x+3)]/([(x-3)(x+3)] * [-(x-3)])
4. Simplify the expression:
[(x^2 - 21x) + (x^2 + 3x)]/(-(x-3)^2)
(2x^2 - 18x)/(-(x-3)^2)
5. Factor and simplify the expression:
2x(x - 9)/-[(x - 3)(x - 3)]
-2x(x - 9)/(x - 3)^2
6. The simplified expression is -2x(x - 9)/(x - 3)^2.
So, the correct answer is -2x(x - 9)/(x - 3)^2.