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# LCD vs NO LCD

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Hi friends,

I understand if I really seem very daft for asking this question, but I'm going to ask anyway...if we have this:

$${x^2 \over 6}-{3x \over2}-{x\over3}+3$$

we get the LCD, which is 6

so we have:

$${x^2 -9x -2x+18}\over6$$

finally we have:

$${x^2 -11x+18}\over6$$

WHY CAN'T WE JUST DO THIS:

we have:

$${x^2 \over 6}-{3x \over2}-{x\over3}+3$$

just multiply with 6 straight through, and get:

$${x^2 -11x+18}$$

NO LCD...

Sorry if this is really a daft question..

Jun 6, 2023

#1
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What you have is an expression, no = sign. so you must get a common denominator.

when you have an equation with an = sign, then you can multiply everything by number,

the reason is the multiplication property of equality requires an equal sign to maintain equation balence.

In your example, notice the top answer still has /6 in it, where in the bottom part, notice the /6 is gone.

Jun 6, 2023
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Hi guest,

yes the answers are different...okay, so it's about the = sign then...I see, thank you for clearing that up for me..I do appreciate..stay well

juriemagic  Jun 7, 2023