# week 15 precalc

this week we finished unit 7 on rational expressions.

In 7.4 we learned how to simplify rational expressions with binomials or trinomials.  first you must factor or simplify any functions in the expression before finding the lowest common denominator.  then by multiplying the numerator with the common denominator you can start to add the like terms of the expression together and make it into one whole fraction.

Ex :

$\frac {6}{v-2} + \frac {7}{2v+7}$

$\frac {12v+42}{(v-2)(2v+7)} + \frac {7v-14}{9v-2)(2v+7)}$

$\frac {19v+28}{(v-2)(2v+7)}$

v cannot equal 2 or $\frac {-7}{2}$

In 7.5 we solved rational equations by eliminating the fractions, bringing everything over to one side and either isolate or factor to find x.

Ex:

$\frac{4}{5x-2} = \frac {3}{4x-1}$

$16x-4=15x-6$

$x=-2$

$x= \frac{2}{5} , \frac {1}{4}$

In 7.6 we solved word problems involved with rational expressions.  With word problems involving time, speed and distance we would use the TSD triangle to help find and equation with variables to help find the average speed.  With problems involving work we need to create a chart that shows the fraction of work done in each period of time.  in these problems, the expression will always equal 1 because in a case of mowing a lawn, you are mowing 1 whole lawn not multiple lawns.