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A rational equation is an
equation in which one or more of the terms is a fractional
one.
When solving these rational equations, we utilize one of two methods
that will eliminate the denominator of each of the terms.
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Method 1 :
(where two fractional terms are equal to each other) |
If the equation is in the form of a
proportion:
you can use "product of the means = product of the extremes"
or "cross-multiplication" to eliminate the denominator,
as in:
 .
Then solve the resulting equation and
check.
For example:
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Cross-multiply to get: |
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Now, solve to find x. |
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Check the answer by
substitution. |
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Work the expressions
to get an equality.
This answer CHECKS! |
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Method 2:
(If the equation is made
up of three or more terms)
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To solve the rational
equation in this method, we:
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| (1) Identify the least
common denominator (LCD), |
| (2) Multiply each side
of the equation by the LCD, simplify, then |
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(3) Solve
the resulting equation, and |
| (4) Check the answer.
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For example:
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Identify the LCD. |
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Multiply
equation
by 12x |
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Distribute the
12x, and simplify |
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Re-write the
equation and solve |
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Check the
answer by substitution
This answer CHECKS! |
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The check is very important in
rational equations, as you can get answers
that do not check in the original
equation.
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Make sure you
check your answers. |
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Look at this example: |
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Find the LCD |
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Multiply by the
LCD, and simplify |
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And solve the
resulting equation |
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Now, check
a
= 1 |
When
substituted into the original
equation, however,
a = 1 yields
an undefined fraction.
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Answer:
No solution |
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How to use
your
TI-83+/84+ graphing calculator with
rational equations.
Click calculator. |
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