i don't understand this fraction please help!
2x - x"2" 3x - 1
________ + _________
6 4
To simplify the given fraction, we need to find a common denominator for the two terms.
The least common multiple (LCM) of 6 and 4 is 12. So, we will rewrite each term with a denominator of 12.
For the first term:
The original denominator is 6, so we need to multiply both the numerator and denominator by 2 to get a denominator of 12.
(2x - x^2) / 6 = (2 * (2x - x^2)) / (6 * 2) = (4x - 2x^2) / 12
For the second term:
The original denominator is 4, so we need to multiply both the numerator and denominator by 3 to get a denominator of 12.
(3x - 1) / 4 = (3 * (3x - 1)) / (4 * 3) = (9x - 3) / 12
Now that both terms have the same denominator of 12, we can add them:
(4x - 2x^2) / 12 + (9x - 3) / 12
To add these fractions, we combine the numerators:
(4x - 2x^2 + 9x - 3) / 12
Now, let's simplify the numerator:
Combine like terms:
(4x + 9x - 2x^2 - 3) / 12
(13x - 2x^2 - 3) / 12
Therefore, the simplified fraction is (13x - 2x^2 - 3) / 12.