1/X +1/x+3=1/2
I don't get LCD/distribution?
To solve the equation 1/X + 1/X+3 = 1/2, you need to find a common denominator, also known as a least common denominator (LCD). In this case, the denominators are X and X+3.
To find the LCD, you need to determine the smallest expression that both X and X+3 can divide evenly into.
In this case, the LCD is X(X+3). This is because every term will need to be multiplied by a factor that equals 1, in order to change the denominators to the LCD.
Now, let's distribute the LCD to each term in the equation:
The first term, 1/X, needs to be multiplied by (X+3)/ (X+3) in order to change its denominator to the LCD:
(1/X) * (X+3)/ (X+3) = (X+3) / (X(X+3))
Similarly, the second term, 1/(X+3), needs to be multiplied by X/ X:
(1/(X+3)) * (X/ X) = X / (X(X+3))
Now, the equation becomes:
(X+3) / (X(X+3)) + X / (X(X+3)) = 1/2
Simplifying further, we get:
(X+3 + X) / (X(X+3)) = 1/2
Combining like terms:
(2X + 3) / (X(X+3)) = 1/2
To eliminate the fractions, you can cross multiply:
2(X(X+3)) = (2X + 3) * (1)
Simplifying further:
2X^2 + 6X = 2X + 3
Rearranging terms:
2X^2 + 6X - 2X - 3 = 0
Simplifying:
2X^2 + 4X - 3 = 0
At this point, you can either attempt to factor the quadratic equation or use the quadratic formula to solve for X.