Express 2x/3-(x-1/4) as a single fraction
To express the expression 2x/3 - (x-1/4) as a single fraction, we need to combine the two fractions into one.
To do this, we need a common denominator for both fractions, which in this case would be 12, since both 3 and 4 divide into 12.
Multiplying the first fraction 2x/3 by 4/4, we get (8x/12).
Next, multiplying the second fraction (x-1/4) by 3/3, we get (3x-3/12).
Combining the fractions, we have (8x/12) - (3x-3/12).
Now, since both fractions have a common denominator of 12, we can combine the numerators: 8x - (3x-3) = 8x - 3x + 3 = 5x + 3.
Therefore, the expression 2x/3 - (x-1/4) can be expressed as a single fraction: (5x + 3)/12.
To express 2x/3 - (x - 1/4) as a single fraction, you need to find a common denominator for the fractions involved.
The denominators we have are 3 and 4. The LCM (Least Common Multiple) of 3 and 4 is 12.
So we can rewrite the expression as:
(8x/12) - ((3x - 1)/12)
Now we can combine the numerators:
8x - (3x - 1)
To simplify further, distribute the negative sign to both terms inside the parentheses:
8x - 3x + 1
Now combine the like terms:
5x + 1
Therefore, 2x/3 - (x - 1/4) can be expressed as (5x + 1)/12.