Simplify into one fraction.
-3/x+2-5/x+3
A. -8x-19/(x+2)(x+3)
B. -8/(x+2)(x+3)**
C. 2/(x+2)(x+3)
D. 2x+1/(x+2)(x+3)
Nope. What did you do?
And use some parentheses:
-3/(x+2) - 5/(x+3)
To simplify the given expression -3/x+2 - 5/x+3 into one fraction, you need to find a common denominator for both fractions and then combine the terms. Here's how you can do that:
Step 1: Find the common denominator.
The denominators in the expression are (x+2) and (x+3). To find the common denominator, you need to factorize the denominators and then multiply them together.
(x+2)(x+3)
Step 2: Adjust the numerators.
To make both fractions have the same denominator, you need to adjust the numerators accordingly. Multiply -3 by (x+3) and multiply -5 by (x+2).
(-3)(x+3) - (5)(x+2)
Step 3: Simplify the expression.
Now, you can simplify the expression by expanding the terms, combining like terms, and writing it as one fraction.
-3(x+3) - 5(x+2) / (x+2)(x+3)
Simplifying further, you get:
-3x - 9 - 5x - 10 / (x+2)(x+3)
Combining like terms, you get:
-8x - 19 / (x+2)(x+3)
Therefore, the simplified expression is -8x - 19 / (x+2)(x+3), which corresponds to answer choice A.