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?
2007-01-25 02:56:57 · 8 answers · asked by Ken H 1 in Science & Mathematics ➔ Mathematics
The reason is because there aren't "sides" in a rational expression. That is,
1/3 + 1/5 = x/3
Multiply both sides by 15 would give us
5 + 3 = 5x
Here's a rational expression:
(x + 3) / (x - 2)
What is it you want to do here; multiply both sides by (x - 2)? But wait; there IS no other side! There's no = sign!
2007-01-25 03:02:08 · answer #1 · answered by Puggy 7 · 0⤊ 1⤋
When solving a rational equation, why it is OK to remove the
denominator by multiplying both sides by the LCD:
It is because multiplying both sides by the same factors (not zero), the equality (another one ) will be maintained but each of the expressions on the two sides do not remain the same.
why can you not do the same operation when simplifying a rational expression :
Because if you do so, the expression will not be equal to the original expression.
2007-01-25 03:13:55 · answer #2 · answered by Anonymous · 0⤊ 1⤋
Because a rational expression is not set equal to something. Keep in mind that whatever you do to one side you must do to the other side; with a rational equation there is an other side, with expression there is not another side.
2007-01-25 03:04:05 · answer #3 · answered by bruinfan 7 · 0⤊ 1⤋
Interesting responses.
If you have the complex expression (8+4i) / (3+2i), the way to "fix this" is to multiply both the top and bottom by (3-2i) to make the denominator a whole number.
So I'm with you. If you multiply a/b by c/c you have not altered the value of the expression since ac/bc = a/b.
I will caution you against dividing or multiplying by variables, though.
2007-01-25 03:06:48 · answer #4 · answered by bequalming 5 · 0⤊ 1⤋
With an EQUATION, you can multiply both sides by the same number (or expression) to simplify.
With an EXPRESSION, you can multiply both "sides" (meaning the top and bottom, or numerator and denominator) by the same number (or expression) to simplify.
it's kind of the same concept.
2007-01-25 03:12:37 · answer #5 · answered by Mathematica 7 · 1⤊ 0⤋
because the rational equation is to have the lcd to multiply both side
2007-01-25 03:00:58 · answer #6 · answered by wnp46 1 · 0⤊ 1⤋
One is an equation. The other is an expression. They are different.
For an equation, you can multiply both sides by a non-zero numbers.
But for an expression, you don't have two sides to balance.
2007-01-25 03:01:15 · answer #7 · answered by sahsjing 7 · 0⤊ 1⤋
earlier initiate those variety of question, ought to bear in mind: "A penny is worth one million cent, a nickel is worth 5 cents, a dime is worth 10 cents and 1 / 4 worth 25 cents" Say has X nickels and Y quarters So, totaling $6.50, get 5X + 25Y = 650 cents 4 greater nickels than quarters, get X = Y + 4 sparkling up those 2 equations to get Y = 21, X = 25 Sue has 25 nickels and 21 quarters
2016-11-27 01:10:22 · answer #8 · answered by sickels 4 · 0⤊ 0⤋