IM Alg2.2.22 Practice: Solving Rational Equations

Identify all values of that make the equation true.

Kiran is solving  for , and he uses these steps: He checks his answer and finds that it isn't a solution to the original equation, so he writes “no solutions.” Unfortunately, Kiran made a mistake while solving. Find his error and calculate the actual solution(s).

Identify all values of that make the equation true.

Is this the graph of  or ? Explain how you know.

Rewrite the rational function  in the form , where  and  are constants.

Elena has a boat that would go 9 miles per hour in still water. She travels downstream for a certain distance and then back upstream to where she started. Elena notices that it takes her 4 hours to travel upstream and 2 hours to travel downstream. The river’s speed is  miles per hour. Write an expression that will help her solve for .