SOLUTION: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational

Algebra ->  Rational-functions -> SOLUTION: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational       Log On


   

Question 52976: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
This idea drives a lot of students nuts. When you have an expression, you don't have an equal sign in which to multiply both sides of the equation by a number and eliminate the denominators.
x%2F2%2Bx%2F3
The best you can do is give the fractions a common denominator by multiplying the numerator and the denominator by a number that will give both fractions the same denominator and combine the numerators:
3%2Ax%2F%283%2A2%29%2B2%2Ax%2F%282%2A3%29
3x%2F6%2B2x%2F6
5x%2F6
Equations enable us to use the fact that we can multiply both sides of the equation by anything (except 0) and not change the value of the equation.
x%2F2%2Bx%2F3=1
6x%2F2%2B6x%2F3=6%2A1
3x%2B2x=6
5x=6
5x%2F5=6%2F5
x=6%2F5
We can solve this same equation by simplifying the left side and then solving for x, but it's extra work with fractions and most of us don't like extra work especially when it involves fractions. You'll recognize the first three lines from the example I gave you on simplified expressions:
3%2Ax%2F%283%2A2%29%2B2%2Ax%2F%282%2A3%29=1
3x%2F6%2B2x%2F6=1
5x%2F6=1
%286%2F5%29%285x%2F6%29=1%286%2F5%29
x=6%2F5
I hope this helps. In short, expressions don't have equal signs so we can't clear our fractions by multiplying both sides of the = sign by the LCD.