To solve rational equations: 1. Multiply each term by the least common denominator to remove denominators. 2. Simplify the resulting equation. 3. Check that any solutions do not make original denominators equal to zero. Follow these steps to clear denominators, simplify the equation, and verify solutions.

1. Solving Rational Equations
Who needs Pythagoras' theorem? by flickr user dullhunk

2. Simplify and state restrictions if any ...
Addition

5. Simplify and state restrictions if any ...
Addition

6. To solve rational equations, follow
these steps:
1. Remove the denominators of the rational expressions by
multiplying each rational expression in the equation by the least
common denominator.
For example, the least common denominator of the equation
is

7. To solve rational equations, follow these steps:
2. Multiply each term by the least common denominator (e.g., 6x(x – 1))
to yield an equation with all denominators equal to 1.
x=3 x=4

8. To solve rational equations, follow
these steps:
3. Check your possible solution(s) for x. Check that neither of these
numbers will cause any of the original denominators to equal 0.
Since the restrictions are x≠1 and x≠0 it follows that x = 3 or x = 4
are the solutions to the original equation.

9. To solve rational equations, follow
these steps:
Note: Be careful not
to confuse a rational
expression and a
rational equation.
When simplifying a rational expression, the denominator remains (unless
it cancels with a common factor in the numerator).
In solving a rational equation, the denominator is cleared by multiplying
both sides by the least common denominator.