Simplify the given expressions and then check your answers with a calculator as in Example 8. Data from Example 8
Simplify the given expressions and then check your answers with a calculator as in Example 8.
Data from Example 8
To graphically check the result of Example 7, we first let y1 equal the original expression and y2 equal the final result. In this case,
Figure 6.2(a) shows y2 (in red) being graphed right over y1 (in blue). Since the graphs are the same, we can consider this as a check (but not as a proof) that the expressions are equivalent.
The table in Fig. 6.2(b) also shows the expressions are equivalent throughout their common domains since the y-values, when they exist, are the same for y1 and y2. The x-values that cause division by zero in either function have undefined y-values and are shown as “ERROR” in the table. It is important to note that although the two functions agree with each other, their domains are different.
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