Subtract and simplify. x/3x+76 - x/9x+21
To subtract and simplify this expression, we first need to find a common denominator for the fractions.
The denominators are 3x+76 and 9x+21.
The least common multiple (LCM) of the denominators is (3x+76)(3).
So, multiply the first fraction by (3)/(3) and the second fraction by (3)/(3):
(x/3x+76) * (3)/(3) - (x/9x+21) * (3)/(3)
This gives us:
3x/9x+228 - 3x/27x+63
Now, we can combine the fractions:
(3x - 3x)/(9x+228) - (3x)/(27x+63)
Since the numerators are the same, we can subtract the fractions:
0/(9x+228) - (3x)/(27x+63)
Simplifying:
0 - (3x)/(27x+63)
-(3x)/(27x+63)
So, the simplified expression is -(3x)/(27x+63).
To subtract and simplify the given expression:
First, let's find a common denominator for the two fractions, which is (3x + 76)(9x + 21):
x/(3x + 76) - x/(9x + 21)
Next, we need to rewrite the numerators with the common denominator:
(x * (9x + 21))/(9x + 21) - (x * (3x + 76))/(3x + 76)
Now, we can combine the numerators over the common denominator:
[9x^2 + 21x - 3x^2 - 76x] / (9x + 21)
Simplifying the numerator by combining the like terms:
(9x^2 - 3x^2 + 21x - 76x) / (9x + 21)
(6x^2 - 55x) / (9x + 21)
Now, we can check if there are any common factors in the numerator and the denominator that could be simplified:
The greatest common factor (GCF) of the numerator is 6x, and the GCF of the denominator is 3:
(6x * (x - 55)) / (3 * (3x + 7))
Finally, the expression is simplified to:
(2x * (x - 55)) / (3x + 7)
To subtract and simplify these fractions, we need to find a common denominator (a common multiple of the denominators) and then combine the numerators.
The denominators in this case are 3x + 76 and 9x + 21. To find a common denominator, we need to find the least common multiple (LCM) of these two expressions.
Let's find the LCM of 3x + 76 and 9x + 21:
1. Factor both expressions:
3x + 76 = 3(x + 25)
9x + 21 = 3(3x + 7)
2. Write down the unique factors of both expressions:
Unique factors of 3(x + 25): 3, (x + 25)
Unique factors of 3(3x + 7): 3, (3x + 7)
3. Multiply the unique factors to get the LCM:
LCM = 3 * (x + 25) * (3x + 7)
Now, we rewrite the fractions with the common denominator and subtract the numerators:
x/(3x + 76) - x/(9x + 21) = (x * 3(3x + 7))/(3 * (x + 25) * (3x + 7)) - (x * (x + 25))/(3 * (x + 25) * (3x + 7))
Next step is to simplify the numerators:
(3x^2 + 7x)/(9x + 21) - (x^2 + 25x)/(3(x + 25))
Now that we have the same denominator, we can subtract the fractions by subtracting the numerators:
[(3x^2 + 7x) - (x^2 + 25x)]/(3(x + 25)(9x + 21))
Simplifying the numerator by combining like terms:
(3x^2 - x^2 + 7x - 25x)/(3(x + 25)(9x + 21)) = (2x^2 - 18x)/(3(x + 25)(9x + 21))
Therefore, the simplified form of the expression is (2x^2 - 18x)/(3(x + 25)(9x + 21)).