IM Alg2.2.22 Lesson: Solving Rational Equations

Jada is working to find values of that make this equation true: She says, “If I multiply both sides by , I find that the solutions are  and , but when I substitute in , the equation does not make any sense.”  Is Jada’s work correct? Explain or show your reasoning.

Why does Jada’s method produce an value that does not solve the equation?

What are the solutions to ?

What are the solutions to ?

How can you solve  by inspection?

How does the denominator influence the solution(s) to ?

Here are a lot of equations. For each one, use what you know about division to identify values of that cannot be solutions to the equation. a.

b.

c.

d.

e.

f.

g.

h.

i.

Without solving, identify three of the equations that you think would be least difficult to solve and three that you think would be most difficult to solve. Be prepared to explain your reasoning.

Choose three equations to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.