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# Subtracting rational expressions: factored denominators

Sal subtracts two rational expressions whose denominators are factored. The denominators aren't the same but they share a factor.

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• sorry i figured out that letter that i thought was a 2/7 is accually a z
• how do I stop getting confused between LCM and GFC
• can you factor by grouping in the numerator at the end?
• Shouldn’t you check to see if the final answer can be simplified? Like maybe he could factor by grouping or something like that on the numerator and check to see if there can be anything that can be cancelled out?
• No, because doing that would change the final answer. If, for example, we found a (z+8) factor to cancel, then our final function would be defined at z=-8, while the original is not, so they're different functions.

But as it happens, the polynomial in the numerator has no linear factors anyway, which you can check with the rational root theorem.
• is that number with a line through it a 2 or a 7? Because it looks like a 2 and a 7 mixed together
• At he inverts the numerator of the second fraction
3(z+8) becomes -3(z+8). Why is this necessary?

Edit: There is subtraction involved so I imagine this is to accommodate the fact that the signs change when combining them. If this was addition the sign change would not be necessary. Am I wrong?
• That is correct. He did invert the coefficient because he wanted to use the addition operator, so he accommodated the fact that one has to change the signs after distributing the subtraction sign.
• How does Sal know not to factor the numerator(I am referring to the final answer). So he would check for common factors to cancel out. Is there a giveaway in expressions that tell you that the numerator and denominator don't have common factors. Or did Sal do this problem beforehand and factored out the numerator and saw that there were no common factors.
• With lots of experience, you may recognize that factoring the numerator would not be helpful. The better approach is to always factor it so you don't miss common factors that can and must be cancelled out.
• How do u find least common denominator with letters and numbers?🤔
(1 vote)
• You just treat variable as one of the factors. For example:
`70 = 2 x 5 x 7`
`6b = 2 x 3 x b`
So, lcd of 70 and 6b is: `2 x 3 x 5 x 7 x b = 210b`
• I still dont get it!! How can you find the LCM if you dont know the denominator in the first place!
• We actually know the denominator, but the only difference is that it is in the form of an algebraic expression rather than integers, so the procedure looks different and complicated. But in fact, it is not
(1 vote)
• Why do you not multiply the 3 with (z+8)(9z-5)(z+6) and only with the (z+8) ?
(1 vote)
• Each fraction needs to be converted to the common denominator: (z+8)(9z-5)(z+6). The factor with 3 in the numerator already has the factors of (9z-5)(z+6) in the denominator. So, we multiply the fraction by the factor that is missing: (z+8)/(z+8).

If you multiplied by (z+8)(9z-5)(z+6), your denominator would become: (9z-5)(z+6)(z+8)(9z-5)(z+6) which is much bigger than the common denominator that you are trying to create.

Hope this helps.