2/x^2-4+3/x^2+x-6+1/x+3
Could someone help me with this fraction? I have tried to answer it over three days now without any luck. If anyone can help please show the steps,so I can see how you got the answer. Thanks in advance!!!
Whenever you post a fraction, you need to insert sufficient parentheses to make sure it is not ambiguous.
You question may remain unanswered for that reason.
To simplify this expression, we need to find a common denominator for the fractions and combine them into one fraction.
The given expression is:
2/x^2 - 4 + 3/x^2 + x - 6 + 1/x + 3
To find the common denominator, we need to factor the denominators of each fraction.
x^2 - 4 can be factored as (x + 2)(x - 2).
x^2 + x - 6 can be factored as (x - 2)(x + 3).
x is already factored as x.
And 3 can be factored as 3.
So the common denominator will be (x + 2)(x - 2)(x + 3).
Now let's rewrite the fractions with the common denominator:
2/x^2 can be written as 2(x + 2)(x - 2)/(x + 2)(x - 2)(x + 3)
3/x^2 + x - 6 can be written as 3/(x + 2)(x - 2)
1/x can be written as 1(x + 2)(x - 2)(x + 3)/(x + 2)(x - 2)(x + 3)
Now we can combine these fractions by adding their numerators:
(2(x + 2)(x - 2) + 3 + 1(x + 2)(x - 2)(x + 3))/(x + 2)(x - 2)(x + 3)
Expanding the numerator:
(2x^2 - 8 + 3 + x^3 + 3x^2 + 6x + x^2 + 2x^3 + 4x^2 + 3x - 4)/(x + 2)(x - 2)(x + 3)
Combining like terms:
(3x^3 + 4x^2 + 6x + 3x^2 + 6x - 9)/(x + 2)(x - 2)(x + 3)
Simplifying further:
(3x^3 + 7x^2 + 12x - 9)/(x + 2)(x - 2)(x + 3)
Therefore, the simplified expression is (3x^3 + 7x^2 + 12x - 9)/(x + 2)(x - 2)(x + 3).