Example 1 Replace T(d) with 45 Multiply 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 Step 1 – get a common denominator for all fractions; factor the denominators and take one of everything: Step 2 – multiply the top of each fraction with what’s not included in the original: Step 3 – once the denominators are the same, you only have to worry about the numerators: Step 4 – simplify and solve: Step 5 – check the original equation for problems in the denominator, and throw out any extraneous solutions.

Example 3 Partial 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.

Ex. 4 Mark 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 4 (cont’d)

Example 5 The excluded value is:zeroRewrite: 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.

HW: Page 247