8.5.1 Solve rational equations and inequalities by hand using algebra.

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8-5 LEARNING GOALS
8.5.1 Solve rational equations and inequalities
by hand using algebra. 8.5.2 Solve rational
equation and inequalities with a graph and table.
A rational equation is an equation that contains
one or more rational expressions and a _________
sign. Solving for x means that you will have x
in for your answer.
Example 1 Solving Rational Equations Solve the
equations. Check your answer.
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An ____________ ____________is a solution that is
not a solution of the original equation. Always
check your solutions by substituting them into
the original equation.
Example 2 Extraneous Solutions
Solve each equation, then check. You can also
use your calculator to check your answers, too.
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Solve the equations, then check.
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Example 5 Using Graphs and Tables to Solve
Rational Equations and Inequalities
A. Solve 3 by using a graph and
a table.
Step 2 Find where the two functions cross (check
with table)
Step 1 Plug in left side to Y1 and right side to
Y2
B. Solve 3 by using a graph and
a table.
Step 2 Find where the two functions cross
determine which x values produce y values less
than or equal to 3.
Step 1 Plug in left side to Y1 and right side to
Y2
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