2.6. Solving Rational Equations http://www.ck12.org
2 xy− 5 y=− 3 x+ 7
y( 2 x− 5 ) =− 3 x+ 7
y=− 23 xx−+ 57Concept Problem Revisited
In order to deal with extra solutions introduced when both sides of an equation are multiplied by a variable, you
must check each solution to see if it makes the denominator of any fraction in the original equation zero. If it does,
it is called an extraneous solution.
Vocabulary
Anextraneous solutionis a “fake” solution to a rational equation that is introduced when both sides of an equation
are multiplied through by zero.
Arational equationis an equation with at least one rational expression.
Arational expressionis a ratio of two polynomial expressions.
Guided Practice
- Solve the following rational equation.
x^3 −x 5 +^4 =x- In electrical circuits, resistance can be solved for using rational expressions. This is an electric circuit diagram
with three resistors. The first resistorR 1 is run in series to the other two resistorsR 2 andR 3 which are run in
parallel. If the total resistanceRis 100 ohms andR 1 andR 3 are each 22 ohms, what is the resistance ofR 2?
The equation of value is: