example 1 replace t(d) with 45 multiply both sides by the denominator solve for d the maximum depth...
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Example 1
Replace T(d) with 45Multiply both sides by the denominator
Solve for d
The maximum depth the diver can go without decompression is approximately 70.8 feet.
(A Rational equation: an equation with a variable in the denominator.)
Example 2
11 aa
111111
aaaaaa
Step 1 – get a common denominator for all fractions; factor the denominators and take one of everything:
11 aa
Step 2 – multiply the top of each fraction with what’s not included in the original:
11
12
11
5
11
11 22
aa
aaa
aa
a
aa
aaa
Step 3 – once the denominators are the same, you only have to worry about the numerators: 12511 22 aaaaaaa
Step 4 – simplify and solve: 225
125122323
222
aaaaaaaa
aaaaaa
1 & 3
013
032
2252
2
aa
aa
aa
aaaa Step 5 – check the original equation for problems in the denominator, and throw out any extraneous solutions.
Example 3Partial fraction: one of the fractions that was added or subtracted to result in a given rational expression. Decomposing fractions is a skill used in calculus and other advanced math classes.
11
1
11
1
11
78
111111
yy
yB
yy
yA
yy
y
yyyyyy
Ex. 4Mark the zeros of the equation with vertical lines on a number line.The zeros are the numbers that would cause the numerator to equal zero.The excluded values are the numbers that would cause the denominator to equal zero.
x = 2 & x = 1
x = 3 & x = 4
The number line is split into 5 different intervals. Test any convenient value within each interval to determine if it is a solution. You don’t even need to
complete the calculations; as long as the value is negative, it is less than zero, so it is a solution.
It is a single # line because there is no “y” in the inequality.
Example 5
012
9
12
10
12
8
a
a
aa
0121212
aaa
The excluded value is:
zero
Rewrite:
The numerical common denominator of 3, 6, & 4 is
12
They all need an “a” as well.Change to = to solve.
Test values in each interval.
0
12
33
12
25
12
42
a
a
aa