[(x-9)/(x^2-9)]-[(1)/(x+3)]
I got (6-x)/(x+3) for answer.
[(2)/(y-3)]+[£¨4£©/(3-y)]
I got (-2)/(y-3) for answer.
I'm not sure about the answers, please check them for me and correct me!
THANKS A LOT!
The first is wrong. I am not certain about the second.
I will be happy to check your work. To do the first one, multiply the second term only by (x-3)/(x-3)
I did mutiply the second term by (x-3)/(x-3), but when I simplify it, I got mess up.
To verify whether your answers are correct, let's simplify each expression step by step.
1. Expression: [(x-9)/(x^2-9)] - [(1)/(x+3)]
First, let's factor the denominator x^2 - 9, which is a difference of squares.
x^2 - 9 = (x + 3)(x - 3)
Now, let's rewrite the expression with the factored denominator:
[(x-9)/((x + 3)(x - 3))] - [(1)/(x + 3)]
To simplify further, we need to find a common denominator. The common denominator is (x + 3)(x - 3). We can rewrite each fraction with this common denominator:
[(x-9)/((x + 3)(x - 3))] - [(1)(x - 3)/((x + 3)(x - 3))]
Now, let's combine the numerators over the common denominator:
[(x - 9) - (x - 3)] / ((x + 3)(x - 3))
Simplifying the numerator:
[x - 9 - x + 3] / ((x + 3)(x - 3))
The x terms cancel out, leaving us with:
[-6] / ((x + 3)(x - 3))
The final answer is:
-6 / ((x + 3)(x - 3))
Therefore, your answer of (6 - x) / (x + 3) is incorrect.
2. Expression: [(2)/(y-3)] + [(4)/(3-y)]
This expression has a difference in the signs between the two fractions. To simplify, we need to find a common denominator. The common denominator is (y - 3)(3 - y), or simply (y - 3)(-1)(y - 3).
Let's rewrite each fraction with the common denominator:
[(2)(-1)(y - 3)/((y - 3)(-1)(y - 3))] + [(4)(y - 3)/((y - 3)(-1)(y - 3))]
Now, let's combine the numerators over the common denominator:
[-2(y - 3) + 4(y - 3)] / ((y - 3)(-1)(y - 3))
Simplifying the numerator:
[-2y + 6 + 4y - 12] / ((y - 3)(-1)(y - 3))
Combining like terms in the numerator:
[2y - 6] / ((y - 3)(-1)(y - 3))
Now, let's simplify further. The numerator can be factored out:
[2(y - 3)] / ((y - 3)(-1)(y - 3))
Canceling out the common factors in the numerator and denominator:
2 / (-1)
The final answer is:
-2
Therefore, your answer of (-2) / (y - 3) is correct.
Please let me know if you have any further questions or need additional clarification!