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Chapter 0: Problem 42

Add or subtract as indicated. $$\frac{8}{x-2}+\frac{2}{x-3}$$

Short Answer

Expert verified
The sum of the fractions \(\frac{8}{x-2}+\frac{2}{x-3}\) is \(10x-28\).

Step by step solution

01

Find the Least Common Denominator (LCD)

In order to add or subtract fractions, they must have the same denominator or in other words, we need a least common denominator (LCD). In this case, the LCD of \(x-2\) and \(x-3\) is their product which is \((x-2)(x-3)\).
02

Rewrite the fractions

Rewrite fractions using the LCD. In this case, the equation turns into \(\frac{8}{x-2}*(x-3)+(x-2)*\frac{2}{x-3}\). The objective here is to make the denominators the same.
03

Simplification

Simplify the resulting expression by multiplying the numerators and getting rid of the denominators. It will result in \(8*(x-3)+2*(x-2)\).
04

Distribution

Distribute 8 in \(8*(x-3)\) and 2 in \(2*(x-2)\), we get \(8x-24+2x-4\).
05

Combine like terms

Combine terms to obtain the final result. The equation simplifies to \(10x-28\) once like terms are combined.

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Most popular questions from this chapter

Factor and simplify each algebraic expression. $$\left(x^{2}+3\right)^{-\frac{2}{3}}+\left(x^{2}+3\right)^{-\frac{5}{3}}$$

This will help you prepare for the material covered in the next section. a. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. b. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. c. Based on your answers to parts (a) and (b), what can you conclude?

Evaluate each algebraic expression for the given value or values of the variable(s). $$6 x-y, for\quad x=3\quad and\quad y=8$$

Give an example of a rational number that is not an integer.

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}+5 x, \text { for } x=6$$
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