[(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!
To check the answers, let's simplify both expressions step by step:
1. Simplify the first expression:
[(x-9)/(x^2-9)] - [1/(x+3)]
To simplify the expression, first factorize the denominator of the first fraction:
[(x-9)/((x+3)(x-3)))] - [1/(x+3)]
Now, let's find a common denominator for both fractions:
[(x-9)/((x+3)(x-3)))] - [(1(x-3))/((x+3)(x-3)))]
Combine the fractions using the common denominator:
[(x-9 - (x-3))/((x+3)(x-3))]
Simplify the brackets:
[(x-9 - x+3)/((x+3)(x-3))]
Combine like terms:
[(-6)/((x+3)(x-3))]
Now we can't simplify it further, so this is the simplified expression.
2. Simplify the second expression:
[2/(y-3)] + [4/(3-y)]
To simplify the expression, first factorize the denominator of the second fraction:
[2/(y-3)] + [4/(-(y-3))]
Simplify the negative sign in the second fraction:
[2/(y-3)] - [4/(y-3)]
Now we have the same denominators, so combine the fractions:
[(2-4)/(y-3)]
Simplify:
[-2/(y-3)]
So, the simplified expression is -2/(y-3).
Now, let's compare the simplified expressions with the answers you got:
1. Simplified expression: [(-6)/((x+3)(x-3))].
Your answer: (6 - x)/(x + 3).
The two expressions are not the same, so your answer is incorrect. The correct simplified expression is -6/((x+3)(x-3)).
2. Simplified expression: [-2/(y-3)].
Your answer: -2/(y-3).
The two expressions are the same, so your answer is correct. Well done!
Therefore, the correct simplified expression for the first question is -6/((x+3)(x-3)), and your answer for the second question is correct as -2/(y-3).