‘clear’라는 단어의 의미는 어떤 일을 하는데 있어서 방해가 되는 일들을 제거하여 그 일을 정상적으로 할 수 있는 단계가 되도록 한다…의 의미입니다. 다른 모든 영어단어들에 있어서와 마찬가지로 “깨끗한”이라는 말로 일대일 대응해서 외우면 안 됩니다.
그렇게 하면 “발포명령, 이륙허가,” 등등… 수십만 가지의 뜻이 되어서 죽을 때까지 공부해도 clear하나도 알지 못합니다. 한 가지 뜻을 수 십만 가지로 바꾸어 놓고 그 중 하나만 아는 바보 같은 공부를 하지 마시기 바랍니다.

어쨌든 이것을 알아야,
To solve an equation by clearing all fractions 라는 말이 해석이 될 겁니다. 이 말의 뜻은 “분수에서 풀이에 걸리는 것들을 모두 제거하여 분수방정식을 풀어 내기..” 라는 뜻이 될 것입니다.

에구, 너무 힘듭니다. 그냥 영어로 쓰겠습니다.

Think back and you’ll get to notice that there is only one problem in a fractional equation to be “cleared”. What is it? How is a fractional equation defined? The variable of an equation is in the denominator. Right?

Now, let’s take a look at another direction of the equation. Please check the following numbers and point the common factor.
(a+2), 4(a+2), t(a+2)

(a+2) is the common factor, you’re with me now, hu?

All these three has at least (a+2) as their common and least factor or multiple. Still with me right?
Naturally (a+2) should be the Least Common Multiple(LCM) of these three different numbers.

Now, let’s get back to where we were!
To clear the fraction, you have to remove the variable from the denominators.
And the LCM of the denominators does always contain the variable.
That’s why you have to multiply the LCM of the denominatorsn to the denominators.

This makes the first step to solve an equation “Multiply each term of the entire equation by the least common multiple of the denominators of the equation."

The following procedure shall be easily understood because no differences are found from the procedure of solution of ordinary equations.

So “Apply the distributive property to remove parentheses,” can be placed as the second step.

Then you should combine like terms on each side of the equation for step 3.
And sort terms to collect the variable or letter terms on one side and number terms on the other for step 4. This can be proceeded by the addition axiom, as you may know of.
For step 5, you should combine like terms on each side of the equation.
And for the last, solve the resulting equation by multiplying by the reciprocal of the coefficient of the variable term or dividing by the coefficient of the variable term. This can be done by the multiplying axiom. Now you’ve arrived at the root of the equation, Good job! Clap! Clap! Clap!

Now, I’m giving you three equations to be solved by clearing all fractions first.

1. Solve (-8) = (4b)/(b-6) by clearing all fractions first.
2. 18 = (4/3x) - (3/2x)
3. (1/3)y + (1/2)y = 20/3

Good luck!

Ernest