Finding Common Demoninators in fractions.
1)
2 4
-- - ---
x^2-16 x^2+x-12
2)
x-3 x+3
---- + ------
x^2+2x-8 x^2+7x+12
Can ANYONE help me with these.
I cant figure out how to get the DEMONINATORS THE SAME!?
Use brackets to write these kind of fractions, the text editor of this board does not seem to recognize more than one space.
Your first denominator is x^2-16, which factors to (x+4)(x-4)
The second denominator is x^2 + x - 12
which factors to (x+4)(x-3)
So the lowest common denominator is
((x+4)(x-4)(x-3)
So multipy the first fraction by (x-3)/(x-3)
and the second by (x-4)/(x-4)
Do the same thing for the second, factor the bottoms and your LCD must contain all of the factors.
Let me know if you got it.
cool brah
To find a common denominator for fractions, you need to identify the factors of each denominator and then multiply them together, taking into account any common factors only once.
Let's break down the steps for each problem:
Problem 1:
The first denominator is x^2 - 16, which can be factored as (x + 4)(x - 4).
The second denominator is x^2 + x - 12, which can be factored as (x + 4)(x - 3).
To find the common denominator, we need to consider all the factors:
Common factors: (x + 4) and (x - 4) from the first denominator, and (x + 4) and (x - 3) from the second denominator.
So, the common denominator is (x + 4)(x - 4)(x - 3).
Now, multiply each fraction by the missing factors to make their denominators the same:
For the first fraction: (2x - 8)/(x^2 - 16)
Multiply by (x - 3)/(x - 3):
[(2x - 8)(x - 3)] / [(x + 4)(x - 4)(x - 3)]
Simplify the numerator if needed.
For the second fraction: (x - 3)/(x^2 + 2x - 8)
Multiply by (x - 4)/(x - 4):
[(x - 3)(x - 4)] / [(x + 4)(x - 4)(x - 3)]
Simplify the numerator if needed.
Problem 2:
The first denominator is x^2 + 2x - 8, which can be factored as (x + 4)(x - 2).
The second denominator is x^2 + 7x + 12, which can be factored as (x + 3)(x + 4).
To find the common denominator, we need to consider all the factors:
Common factors: (x + 4) from both denominators, (x - 2), (x + 3) from the second denominator.
So, the common denominator is (x + 4)(x - 2)(x + 3).
Now, multiply each fraction by the missing factors to make their denominators the same:
For the first fraction: (x - 3)/(x^2 + 2x - 8)
Multiply by (x + 3)/(x + 3):
[(x - 3)(x + 3)] / [(x + 4)(x - 2)(x + 3)]
Simplify the numerator if needed.
For the second fraction: (x + 3)/(x^2 + 7x + 12)
Multiply by (x - 2)/(x - 2):
[(x + 3)(x - 2)] / [(x + 4)(x - 2)(x + 3)]
Simplify the numerator if needed.
Remember to simplify your final answer if possible.