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Chapter 0: Problem 65

Simplify each complex rational expression. $$\frac{x-\frac{x}{x+3}}{x+2}$$

Short Answer

Expert verified
\(\frac{-3}{x+2}\)

Step by step solution

01

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.
02

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.
03

Express the Denominator

No simplification is necessary for the denominator because it's already in simplest form. It remains \(x+2\).
04

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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Most popular questions from this chapter

A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula $$h=4+60 t-16 t^{2}$$ describes the ball's height above the ground, \(h,\) in feet, \(t\) seconds after it was kicked. Use this formula to solve Exercises \(19-20 .\) What was the ball鈥檚 height 3 seconds after it was kicked?

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Fill in each box to make the statement true. Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

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