I'm trying to perform the indicated operations, and reduce to lowest terms, but I'm not sure if I got the correct answer. The question is y-5/(x^2+5x)+(xy+5y) + 1/x+y - 2/x+5....I got y-6, but am not sure if that is correct.
Are you the same James who posted several versions of this yesterday?
http://www.jiskha.com/display.cgi?id=1269297854
If so, it is an improvement, but still not too clear.
I think that (x^2+5x)+(xy+5y) probably should be the entire denominator of the first fraction, you didn't type it that way, so I will read the question this way ....
(y-5)/[(x^2+5x)+(xy+5y)] + 1/(x+y) - 2/(x+5)
= (y-5)/[x(x+5)+y(x+5)] + 1/(x+y) - 2/(x+5)
= (y-5)/[(x+5)(x+y)] + 1/(x+y) - 2/(x+5)
now we have (x+5)x+y) as a common denominator, so
=(y-5)/[(x+5)(x+y)] + (x+5)/[(x+5)(x+y)] - 2(x+y)/[(x+5)(x+y)]
= (y-5 + x + 5 - 2x - 2y)/(x+5)(x+y)]
= (-x - y)/[(x+5)(x+y)]
= -(x+y)/[(x+5)(x+y)]
= -1/(x+5)
To simplify the given expression and reduce it to lowest terms, let's break it down step by step:
1. Start by combining like terms in each fraction separately.
In the first fraction: y - 5 / (x^2 + 5x)
In the second fraction: (xy + 5y) / (x + y)
In the third fraction: 1 / x + y
In the fourth fraction: 2 / x + 5
2. Next, find a common denominator for all the fractions. In this case, we can use (x^2 + 5x)(x + y)(x + 5) as the common denominator.
3. Adjust each fraction accordingly to have the common denominator.
In the first fraction: (y - 5)(x + y)(x + 5) / (x^2 + 5x)(x + y)(x + 5)
In the second fraction: (xy + 5y)(x^2 + 5x) / (x + y)(x^2 + 5x)(x + 5)
In the third fraction: (x + 5)(x + y) / (x^2 + 5x)(x + y)(x + 5)
In the fourth fraction: 2(x^2 + 5x)(x + y) / (x^2 + 5x)(x + y)(x + 5)
4. Combine the fractions over the common denominator.
(y - 5)(x + y)(x + 5) + (xy + 5y)(x^2 + 5x) + (x + 5)(x + y) - 2(x^2 + 5x)(x + y) / (x^2 + 5x)(x + y)(x + 5)
5. Simplify the resulting expression.
Expand and combine like terms in the numerator:
[(y - 5)(x^2 + 5x)(x + y)(x + 5) + (xy + 5y)(x + 5)(x^2 + 5x) + (x + 5)(x + y)(x^2 + 5x) - 2(x^2 + 5x)(x + y)] / (x^2 + 5x)(x + y)(x + 5)
Now, if you compute the numerator and denominator further, you should get the simplified expression.