Subtract and simplify. Show your work.
3/x^2-3x - x/3x-9
To simplify the expression (3/x^2 - 3x) - (x/3x - 9), we need to find a common denominator and combine like terms.
For the first term, the common denominator is x^2, so we multiply the numerator and denominator of 3/x^2 by x to get 3x/x^2.
For the second term, the common denominator is 3x, so we multiply the numerator and denominator of -x/3x by -1 to get x/3x.
Now, let's rewrite the expression with the common denominators:
(3x/x^2 - x/3x) - (x/3x - 9)
Next, let's simplify the terms inside the parentheses:
(3x - x^2) - (x - 9(3x))
Expanding the second term inside the parentheses:
= 3x - x^2 - x + 27x
Combining like terms:
= (3x - x) - x^2 + 27x
Simplifying further:
= 2x - x^2 + 27x
Finally, let's reorder the terms in descending order of degree:
= -x^2 + 29x
Therefore, the simplified expression is -x^2 + 29x.
To subtract and simplify the expression (3/x^2 - 3x) - (x/3x - 9), we will simplify each part separately and then combine the simplified terms.
First, let's simplify the first part: 3/x^2 - 3x.
To combine the terms, we need a common denominator. The denominator of the first term is x^2, and the denominator of the second term is 1.
So, the common denominator is x^2.
Now, we can rewrite the expression with the common denominator:
(3/x^2) - (3x/x^2)
Next, we can subtract the two terms by keeping the same denominator:
(3 - 3x) / x^2
Now, let's simplify the second part: x / (3x - 9).
This expression doesn't require further simplification.
Now, let's combine the two simplified expressions:
(3 - 3x) / x^2 - x / (3x - 9)
To combine these fractions, we need a common denominator for both terms.
The common denominator is x^2(3x - 9).
Let's rewrite the expression using the common denominator:
[(3 - 3x)(3x - 9)] / [x^2(3x - 9)] - (x * x^2) / [x^2(3x - 9)]
Next, let's distribute and simplify the numerators:
[(9 - 27x + 27x - 81) - (x^3)] / [x^2(3x - 9)]
Simplifying the numerator gives:
(-x^3 - 81) / [x^2(3x - 9)]
Therefore, the simplified expression is (-x^3 - 81) / [x^2(3x - 9)].
To subtract and simplify the given expression: 3/x^2-3x - x/3x-9, we need to find a common denominator for both fractions.
First, let's factor the denominators:
x^2-3x can be factored as x(x-3)
3x-9 can be factored as 3(x-3)
Now, the common denominator is (x(x-3))(3(x-3)).
Next, we need to rewrite the fractions with the common denominator:
3/(x(x-3)) - x/(3(x-3))
To subtract the fractions, we can simplify them by multiplying the numerator and denominator of each fraction by the necessary factors to obtain the common denominator.
For the first fraction, we multiply the numerator and denominator by 3:
(3 * 3)/((3)(x(x-3))) - x/(3(x-3))
Simplify the first fraction:
9/(3x(x-3)) - x/(3(x-3))
Now, subtract the fractions:
(9 - x)/(3x(x-3))
So, the simplified expression after subtraction is (9 - x)/(3x(x-3)).