So firstly, we have to make all the denominators the same. To do this, we need to find their LCD, or lowest common denominator. In this case, the LCD is gonna be 6(x + 3). With each fraction, multiply the numerator and denominator by the term that will get the denominator to the LCD:
Now with all the denominators the same, we can cancel them out by multiplying both sides by 6(x + 3):
Next, solve the multiplications:
Next, combine like terms:
Next, subtract both sides by 3x and add both sides by 9:
Next, we want to make the right side of the equation a perfect square. To find the constant of the soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Add the result onto both sides of the equation:
Now, factor the right side:
Next, square root both sides of the equation:
Next, add both sides by 1.5:
Lastly, solve the left side twice - once with the plus sign and once with the minus sign:
<u>In short, x = 0 and 3.</u>