i am having trouble on solving fractional equations such as:
2 3 7
______ + _____ = ______________
x+3 x+4 x^2 +7x+12
factor the right side denominator, then look for what factors make up a common denominator. For each fraction, multiply the numerator and denominator with the factors of the lcd not present. Look at this example:
http://www.themathpage.com/alg/add-algebraic-fractions.htm
To solve the fractional equation, follow these steps:
1. Factor the right side denominator, which is x^2 + 7x + 12.
In this case, the factors are (x + 3)(x + 4).
2. Look for the factors that make up a common denominator.
For the fractions on the left side, the common denominator is (x + 3)(x + 4).
3. Multiply the numerator and denominator of each fraction with the factors of the least common denominator (lcd) not present in each fraction.
For the fraction 2/(x + 3), multiply the numerator and denominator by (x + 4) to get (2(x + 4))/((x + 3)(x + 4)).
For the fraction 3/(x + 4), multiply the numerator and denominator by (x + 3) to get (3(x + 3))/((x + 3)(x + 4)).
4. Combine the fractions by adding the numerators and leaving the denominator as it is.
(2(x + 4) + 3(x + 3))/ ((x + 3)(x + 4)) = (2x + 8 + 3x + 9)/((x + 3)(x + 4))
5. Simplify the numerator by combining like terms.
(2x + 3x + 8 + 9)/((x + 3)(x + 4)) = (5x + 17)/((x + 3)(x + 4))
Thus, the solution to the fractional equation is (5x + 17)/((x + 3)(x + 4)).