Problem 65
Question
Simplify each complex rational expression. $$\frac{x-\frac{x}{x+3}}{x+2}$$
Step-by-Step Solution
Verified Answer
\(\frac{-3}{x+2}\)
1Step 1: Simplify the Numerator
The first step to simplifying the complex rational expression is to simplify the numerator of the overall fraction. Aim to get rid of the fraction in the numerator by multiplying it by the denominator which is \(x+3\) in this case. Therefore, \(x-\frac{x}{x+3}\) becomes \(x-(x+3)\). It's important to make sure to pay attention to the minus sign in front of the fraction, because it will propagate to all the terms of the simplified fraction, changing the sign of each term.
2Step 2: Simplify the Expression
Now the expression will be in the form of \(x-x-3\). Apply basic algebraic operations and add like terms. The final term is \(-3\). The next aim is to simplify the denominator.
3Step 3: Express the Denominator
No simplification is necessary for the denominator because it's already in simplest form. It remains \(x+2\).
4Step 4: Final Simplification
The final form of the expression is the simplified numerator, \(-3\), divided by the denominator, \(x+2\), which is \(\frac{-3}{x+2}\).
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