Simplify 1/2x-3/x+6
taking it exactly the way you wrote it, the LCD is 2x
(1/2)x - (3/x) + 6
= ( x^2 - 6 + 2x)/(2x)
If you meant
1/(2x) - 3/(x+6) it would be different, but I don't want to guess what you mean
BTW, I would classify the opening expression as simplified enough.
Last term in the numerator should have been 12x
( x^2 - 6 + 12x)/(2x)
To simplify the expression (1/2x) - (3/x) + 6, we need to find a common denominator for the two fractions.
The common denominator for 2x and x is 2x. To achieve this, we multiply the first fraction by (x/x) and the second fraction by (2/2):
(1/2x) * (x/x) - (3/x) * (2/2) + 6
Now we can simplify the expression:
(x/2x) - (6/2x) + 6
Next, we combine the like terms in the numerators:
(x-6)/2x + 6
To simplify further, we can find a common denominator for 2x and 1:
(x-6 + (6*2x))/(2x)
Simplifying inside the parentheses:
(x-6 + 12x)/(2x)
Combining like terms in the numerator:
(13x-6)/(2x)
And there you have it, the simplified expression is (13x-6)/(2x).