Add and reduce to lowet terms
m/x^2-9 + 1/3x-9
I need help on this problem. i'm not sure what to do
(3x+16) (4x+219)
To add and reduce the given fractions to lowest terms, you need to find a common denominator for both fractions. The denominators in this case are (x^2 - 9) and (3x - 9).
To find the common denominator, you need to factor the expressions in the denominators. Here's how you do it:
1. Factor the first denominator (x^2 - 9):
x^2 - 9 is a difference of squares, which can be factored as (x - 3)(x + 3).
2. Factor the second denominator (3x - 9):
3x - 9 can be simplified by factoring out the greatest common factor, which is 3.
3x - 9 = 3(x - 3)
Now that you have factored the denominators, the common denominator will be the product of both factors:
Common denominator = (x - 3)(x + 3)(x - 3)
Next, you need to write each fraction with the common denominator:
m / (x^2 - 9) = m / [(x - 3)(x + 3)]
1 / (3x - 9) = 1 / [3(x - 3)]
Now, multiply the numerator and denominator of each fraction by the missing factors needed to make them equal to the common denominator.
For the first fraction:
m / [(x - 3)(x + 3)] * ([3(x - 3)]) / ([3(x - 3)])
For the second fraction:
1 / [3(x - 3)] * [(x + 3)] / [(x + 3)]
Simplifying each fraction:
1. m / [(x - 3)(x + 3)] * ([3(x - 3)]) / ([3(x - 3)]) = 3m(x - 3) / [(x - 3)(x + 3)]
2. 1 / [3(x - 3)] * [(x + 3)] / [(x + 3)] = (x + 3) / [3(x - 3)(x + 3)]
Now you can combine the fractions:
(3m(x - 3) + (x + 3)) / [(x - 3)(x + 3)]
This resulting fraction can be simplified further by combining like terms and canceling out common factors.
Note: It's important to mention that without a specific value assigned to 'm', we cannot simplify the fraction further and reduce it to lowest terms.