Solving Rational Equations

Solving Rational Equations

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.
Method 1 :
4/x = 9/x-2
(where two fractional terms are equal to each other)

If the equation is in the form of a proportion:

a/b = c/d
you can use “product of the means = product of the extremes”  or “cross-multiplication” to eliminate the denominator,

as in: a.d = b.c

Then solve the resulting equation and check.

For example: 4/x = 9/x-2

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To solve the rational equation in this method, we:

(1) Identify the least common denominator (LCD),
(2) Multiply each side of the equation by the LCD, simplify, then
(3) Solve the resulting equation, and
(4) Check the answer.

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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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