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Chapter 7: Problem 78

Explain how to subtract rational expressions when denominators are the same. Give an example with your explanation.

Short Answer

Expert verified
To subtract two rational expressions with the same denominator, keep the denominator and simply subtract the numerators. For instance, \(\frac{5}{7} - \frac{3}{7} = \frac{2}{7}\).

Step by step solution

01

Identify Like Denominators

The first step is to identify if the rational expressions have the same denominators, this is important as it allows us to carry out the subtraction operation. Suppose we have two rational expressions \(\frac{a}{d}\) and \(\frac{b}{d}\) then both expressions have the same denominator (\(d\)).
02

Subtract the Numerators

Given that the denominators are the same, we keep the denominator and subtract the numerators of the two expressions. In this case, we subtract \(b\) from \(a\). Thus the expression becomes \(\frac{a - b}{d}\).
03

Simplify the Resulting Expression

Simplify the resulting rational expression by reducing it to its lowest terms. This often involves factoring the numerator and denominator, and then cancelling out common factors.
04

Example

Let's consider an example: \(\frac{5}{7} - \(\frac{3}{7}\). Here, \(\frac{5}{7}\) and \(\frac{3}{7}\) have the same denominator, so we subtract the numerators: \(\frac{5 - 3}{7} = \(\frac{2}{7}\), which is the answer and doesn't need further simplification.

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Most popular questions from this chapter

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}+4 x+3}{x+2}-\frac{5 x+9}{x+2}=x-2, x \neq-2$$

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

Anthropologists and forensic scientists classify skulls using $$ \frac{L+60 W}{L}-\frac{L-40 W}{L} $$ where \(L\) is the skull's length and \(W\) is its width. a. Express the classification as a single rational expression. b. If the value of the rational expression in part (a) is less than \(75,\) a skull is classified as long. A medium skull has a value between 75 and \(80,\) and a round skull has a value over \(80 .\) Use your rational expression from part (a) to classify a skull that is 5 inches wide and 6 inches long.

Describe how to identify the corresponding sides in similar triangles.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.
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