I'm looking to see if I did this right or not. ((y-5)/((x^2+5x)(x^2+5y)))+((1)/(x+y))-((2)/(x+5)) = ((y-5)/(x+y)(x+5))+((1(x+5)/(x+y)(x+5))-((2(x+y)/(x+y)(x+5)) = ((y-5)+1(x+5)-2(x+y)/(x+y)(x+5)) = y-6 ????
To determine if you simplified the given expression correctly, let's evaluate it step by step:
Step 1: Simplify the numerator and denominator separately.
- Numerator: Rewrite the expressions in a simplified form.
(y - 5) does not simplify further.
- Denominator: Multiply the two sets of parentheses separately.
(x^2 + 5x)(x^2 + 5y) = x^4 + 5xy + 5x^3 + 25y
(x + y)(x + 5) = x^2 + 5x + xy + 5y
Step 2: Simplify the entire expression.
((y - 5)/(x^2 + 5x)(x^2 + 5y)) + (1/(x + y)) - (2/(x + 5))
= ((y - 5)/(x^4 + 5xy + 5x^3 + 25y)) + (1/(x^2 + 5x + xy + 5y)) - (2/(x + 5))
Step 3: To combine the fractions, find a common denominator.
The common denominator for the three fractions is (x^4 + 5xy + 5x^3 + 25y)(x^2 + 5x + xy + 5y)(x + 5).
Step 4: Rewrite each fraction with the common denominator.
= ((y - 5)(x^2 + 5x + xy + 5y))/((x^4 + 5xy + 5x^3 + 25y)(x^2 + 5x + xy + 5y))
+ ((1(x^4 + 5xy + 5x^3 + 25y)(x + 5))/((x^4 + 5xy + 5x^3 + 25y)(x^2 + 5x + xy + 5y)))
- ((2(x^2 + 5x + xy + 5y)(x^2 + 5x + xy + 5y))/((x^4 + 5xy + 5x^3 + 25y)(x^2 + 5x + xy + 5y)))
Step 5: Combine the numerators.
= ((xy^2 + 5xy + x^2y + 5y - 5x^2 - 25x)/(x^4 + 5xy + 5x^3 + 25y)(x^2 + 5x + xy + 5y))
Step 6: Simplify further, if possible.
The expression y - 6 cannot be obtained from the previous steps, so y - 6 is not the correct simplification of the given expression.
In conclusion, y - 6 is not the correct simplification of the original expression.