Question

When solving a rational equation what is the first step we must always take? Illustrate with an example how you clear the rational equation of fractions.

Answer 1

You want to look for the least common multiple of all the denominators. Once you find it, multiply everything by that number, and all the fractions will go away.
Example:
\[x^{3}+\frac{1}{3}x^{2}+\frac{1}{7}x+\frac{1}{21} = 0\]
The lcm of 3, 7, and 21 is 21. So when I multiply everything by 21 I get:
\[21x^{3}+\frac{21}{3}x^2+\frac{21}{7}x+\frac{21}{21}=0\]
\[\Rightarrow 21x^{3}+7x^{2}+3x+1 = 0\]
No more fractions :)