(9/x)-(9/(x^2 + x))
To simplify the expression (9/x) - (9/(x^2 + x)), we need to find a common denominator for the two fractions.
The common denominator will be x*(x+1) since it covers both x and (x^2 + x).
Now, let's rewrite the expression with the common denominator:
(9/x) - (9/(x^2 + x)) = (9(x+1)/(x*(x+1))) - (9x/(x*(x+1)))
Next, we can combine the fractions with the same denominator:
= (9(x+1) - 9x)/(x*(x+1))
Simplifying further:
= (9x + 9 - 9x)/(x*(x+1))
= 9/(x*(x+1))
Therefore, the simplified expression is 9/(x*(x+1)).
To simplify the expression (9/x) - (9/(x^2 + x)), we need to find a common denominator for the fractions.
The common denominator for these fractions is x(x^2 + x).
Now, let's rewrite the fractions using the common denominator:
(9(x^2 + x)/(x(x^2 + x))) - (9x/(x(x^2 + x)))
Simplifying further, we have:
(9x^2 + 9x - 9x)/(x(x^2 + x))
Combining like terms, we get:
(9x^2)/(x(x^2 + x))
Finally, we can simplify the expression to:
9x/(x^2 + x)
To simplify the expression (9/x) - (9/(x^2 + x)), you will need to find a common denominator for the two fractions.
First, identify the LCD (Least Common Denominator) by finding the LCM (Least Common Multiple) of the denominators x and x^2 + x.
The prime factorization of x is: x = x^1
The prime factorization of x^2 + x is: x^2 + x = x(x + 1)
Next, take the maximum exponent for each prime factor present in either denominator:
For x, the highest exponent is 1.
For x^2 + x, the highest exponent of x is 1, and there is no other prime factor.
So, the LCD of x and x^2 + x is x(x + 1).
Now, let's rewrite each fraction with the common denominator of x(x + 1):
(9/x) - (9/(x^2 + x)) = (9 * (x + 1)/(x * (x + 1))) - (9 * x/(x * (x + 1)))
Next, simplify the numerators by distributing:
(9 * (x + 1)/(x * (x + 1))) - (9 * x/(x * (x + 1))) = (9x + 9)/(x * (x + 1)) - (9x)/(x * (x + 1))
Now, combine the two fractions:
(9x + 9 - 9x)/(x * (x + 1)) = 9/(x * (x + 1))
So, the simplified expression is 9/(x * (x + 1)).