I am having trouble with this.
Add (simplify if possible)
(x^2 + 11x)/(x^2 - 3x) + (x^2 - 6x)/(x^2 - 3x)
I actully came up with two possible answers.
(2x+5)/x-3 and (2x^2-5)/x-6x
I'm not sure which answer is correct.
To simplify the given expression and determine the correct answer, you need to combine the two fractions over a common denominator. In this case, the common denominator is (x^2 - 3x).
Let's break down the steps to simplify the expression:
Step 1: Find the common denominator.
Both fractions, (x^2 + 11x)/(x^2 - 3x) and (x^2 - 6x)/(x^2 - 3x), already have the same denominator: (x^2 - 3x).
Step 2: Add the fractions.
To add the fractions, combine the numerators over the common denominator:
((x^2 + 11x) + (x^2 - 6x))/(x^2 - 3x)
Simplifying the numerator:
(x^2 + 11x + x^2 - 6x)/(x^2 - 3x)
(2x^2 + 5x)/(x^2 - 3x)
Now let's simplify further if possible:
Step 3: Factor out common terms (if possible).
In the numerator, the terms 2x^2 and 5x do not share any common factors, so we cannot factor them out.
Step 4: Check for any common factors in the numerator and denominator.
Both the numerator and denominator have an x in each term, so we can factor out x:
x(2x + 5)/(x^2 - 3x)
Therefore, the simplified form of the expression is:
(2x + 5)/(x - 3x)
Now we can simplify the denominator by factoring out x:
(2x + 5)/x(1 - 3)
Simplifying further:
(2x + 5)/x(-2)
Now we have the final simplified expression:
(2x + 5)/-2x
So, the correct answer is (2x + 5)/-2x, or you can also write it as -(2x + 5)/2x.