Simplify.
−6(1 over 4x−2 over 3x+5 over 6x)
−x
−2 and 1 over 2x
3 over 4x
2x
To simplify the expression −6(1/4x-2/3x+5/6x), we can first simplify each individual term in the parentheses:
1/4x can be rewritten as 1/(4x)
2/3x can be rewritten as 2/(3x)
5/6x can be rewritten as 5/(6x)
Now substituting these simplified terms back into the expression:
−6(1/(4x)-2/(3x)+5/(6x))
Next, we need to find a common denominator for the fractions in the parentheses. The least common multiple of 4, 3, and 6 is 12. Multiplying each fraction by the appropriate factor to give them a denominator of 12:
−6(3/(12x)-8/(12x)+10/(12x))
Simplifying the numerators:
−6(3-8+10)/(12x)
−6(5)/(12x)
Finally, simplifying the numerator of the expression:
−30/(12x)
This can be further simplified by dividing the numerator and denominator by their greatest common factor, which is 6:
-5/(2x)
Therefore, the simplified expression is -5/(2x).
To simplify −6(1/4x − 2/3x + 5/6x), we need to combine the fractions with the same denominator.
First, we find a common denominator for 4x, 3x, and 6x, which is 12x.
The given expression can be rewritten as:
−6((3/12x) − (8/12x) + (10/12x))
Next, we combine the fractions:
−6((3 − 8 + 10) / 12x)
−6(5 / 12x)
Finally, we distribute −6 to the fraction:
−6 * 5 / 12x
−30 / 12x
Therefore, the expression −6(1/4x − 2/3x + 5/6x) simplifies to −30/12x, or −5/2x.
To simplify the expression −6(1/4x-2/3x+5/6x), we need to distribute the -6 to each term inside the parentheses and then combine like terms.
First, distribute -6 to each term:
−6 * (1/4x) = -6/4x = -3/2x
−6 * (-2/3x) = 12/3x = 4/x
−6 * (5/6x) = -30/6x = -5/x
Now, rewrite the expression with the distributed terms:
−3/2x + 4/x - 5/x
Next, combine like terms. Since all the terms have the same denominator (x), we can combine them:
(−3/2 + 4 - 5)/x = (−3/2 + 4 - 5)/x = (-3/2 + 8 - 10)/x = (-5/2)/x = -5/2x
Therefore, the simplified expression is -5/2x.