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Chapter 0: Problem 92

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

Short Answer

Expert verified
Therefore, \(\frac{3}{x+5}+\frac{7}{x+2} = \frac{10x+41}{(x+2)(x+5)}\)

Step by step solution

01

Identify and List the Denominators

In this instance, the denominators are \(x+5\) and \(x+2\). Write these two expressions out.
02

Calculate the Least Common Denominator (LCD)

Since the two given expressions do not have any common factors, the LCD will be the product of the two denominators. Therefore, \(LCD = (x+5)(x+2)\).
03

Re-write the Expression with the LCD

Re-write each fraction with the LCD as the denominator. Multiply the numerator and the denominator of each fraction by the missing factor from the LCD. This gives: \[\frac{3}{x+5} = \frac{3*(x+2)}{(x+5)(x+2)} = \frac{3x+6}{(x+5)(x+2)}\;\] and \[\frac{7}{x+2} = \frac{7*(x+5)}{(x+5)(x+2)} = \frac{7x+35}{(x+5)(x+2)}\].
04

Perform the Addition

Now add the two fractions together: \[\frac{3x+6}{(x+2)(x+5)}+ \frac{7x+35}{(x+2)(x+5)} = \frac{3x + 6 + 7x + 35}{(x+2)(x+5)} = \frac{10x+41}{(x+2)(x+5)}\].

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Most popular questions from this chapter

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)

The mass of one hydrogen atom is \(1.67 \times 10^{-24}\) gram. Find the mass of \(80,000\) hydrogen atoms. Express the answer in scientific notation.

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

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