Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	Let's use the denominators for both fractions	18,488	79	[]
student	ok	18,488	80	[]
volunteer	So the denominator for fraction 1 is 1+x^2	18,488	81	[]
student	yes	18,488	82	[]
volunteer	Since x^2 is greater than or equal to 0, 1+x^2 is greater than 0	18,488	83	[]
student	yeah	18,488	84	[]
volunteer	Now for fraction 2, the denominator is x^3-x. We need to check to see if this expression is zero or not	18,488	85	[]
student	yep	18,488	86	[]
volunteer	So we set this expression equal to zero	18,488	87	[]
student	yep	18,488	88	[]
volunteer	So when we solve for 0, we get x=1, x=-1, and x=0	18,488	89	[]
volunteer	Therefore, the domain is {-1,0,1}	18,488	90	[]
student	ok	18,488	91	[]
student	why cant we sex x^2+1=0	18,488	92	[]
volunteer	We don't set x^2+1 to zero because it has no real solution	18,488	93	[]
student	how come?	18,488	94	[]
volunteer	Because when you do set this equal to zero you get x^2=-1	18,488	95	[]
volunteer	The square of any real number is always positive but -1 is negative	18,488	96	[]
student	what if when we multipled we got x^2=1	18,488	97	[]
volunteer	Multiplied when?	18,488	98	[]
student	what if isntead of x^2+1	18,488	99	[]
student	we had x^2-1=0	18,488	100	[]
volunteer	But that isn't the denominator in the first fraction of this problem	18,488	101	[]
student	what if it was	18,488	102	[]
volunteer	x^2+1=0 has no real solutions because x^2+1 is always greater than zero	18,488	103	[]
student	what if x^2-1	18,488	104	[]
student	does it have a solution	18,488	105	[]
volunteer	x^2 is greater than or equal to zero, therefore 1+x^2 is greater than zero	18,488	106	[]
volunteer	It has no restrictions	18,488	107	[]
student	yeah	18,488	108	[]
student	so whats domain	18,488	109	[]
student	of x^2-1=0	18,488	110	[]
volunteer	The domain of x^2-1=0 is all real numbers	18,488	111	[]
volunteer	Equations don't have a domain	18,488	112	[]
student	im saying if in denominatoe	18,488	113	[]
student	denominator	18,488	114	[]
volunteer	We don't look at individual equations and find the domains of them	18,488	115	[]
volunteer	Rather, we tried to find any restrictions for both equations and create a domain from that.	18,488	116	[]
student	yes what if x^2-1=0 so know in future	18,488	117	[]
student	how to solve	18,488	118	[]
volunteer	I'm confused on what your asking. Are you asking to solve for its solutions?	18,488	119	[]
student	i wanna know if was our domain]	18,488	120	[]
student	what domain would be	18,488	121	[]
volunteer	The domain is -1,0,1	18,488	122	[]
student	no '	18,488	123	[]
volunteer	Okay, let me rephrase. When you have a fraction, look for where the denominator equals zero	18,488	124	[]
student	cause x^2-1=0	18,488	125	[]
volunteer	The domain of x^2-1=0 is all real numbers. All polynomials (like x^2) can be defined on a number line, therefore making it all real numbers	18,488	126	[]
student	you cant do all real numbers	18,488	127	[]
volunteer	I'm confused what do you mean you can't do all real numbers?	18,488	128	[]
student	Step 1: Set denominator equal to zero and solve: 𝑥 2 − 1 = 0 x 2 −1=0 𝑥 2 = 1 x 2 =1 𝑥 = ± 1 x=±1 Step 2: Exclude these from the domain. Domain: All real numbers except 𝑥 = 1 x=1 and 𝑥 = − 1 x=−1.'	18,488	129	[]
volunteer	1 and -1 are just solutions, they aren't excluded from the domain	18,488	130	[]
student	they are the restrictions	18,488	131	[]
student	fpor x	18,488	132	[]
student	for	18,488	133	[]
volunteer	So restrictions occur when you have denominators or square roots of negative numbers	18,488	134	[]
volunteer	x^2 is a polynomial, and they work everywhere on a real line.	18,488	135	[]
student	im saying if a denomnator	18,488	136	[]
student	if x^2+1=-0	18,488	137	[]
student	in a random denom	18,488	138	[]
volunteer	There is no negative zero	18,488	139	[]
student	yes ik	18,488	140	[]
student	x^2+1=0	18,488	141	[]
volunteer	You don't set it equal to zero	18,488	142	[]
student	yes you do	18,488	143	[]
student	to find domain	18,488	144	[]
volunteer	Yes, you're right! Sorry, I'm getting confused here. But there are no real solutions	18,488	145	[]
volunteer	Because you can't have x^2=-1	18,488	146	[]
volunteer	Therefore the domain is still all real numbers	18,488	147	[]
student	what about x^2=1	18,488	148	[]
student	can you have that?	18,488	149	[]
volunteer	That would be when you have x^2-1=0 and you solve for zero	18,488	150	[]
volunteer	You get x=1 and x=-1 therefore domain is all real numbers except -1 and 1	18,488	151	[]
student	ok	18,488	152	[]
student	and you can have x^2-1=0 for this problem if we swicthed up the sign from + to -	18,488	153	[]
student	so then that would be domain for our problem if we had a diff sign	18,488	154	[]
volunteer	Yes but it would be a different problem at that point. Different problems give us different domains.	18,488	155	[]
volunteer	You can't switch signs in problems otherwise it will complicate future steps.	18,488	156	[]
student	yes but if we had 1-x^2 instead of 1+x^2	18,488	157	[]
student	that would be the domain	18,488	158	[]
student	for this problem	18,488	159	[]
student	if we subituted	18,488	160	[]
volunteer	Sure	18,488	161	[]
student	ok so im correct if we sub that would be domain	18,488	162	[]
student	for this equatiojn	18,488	163	[]
volunteer	Yes, if you change the denominator you get a different result for domain	18,488	164	[]
volunteer	The combinations are limitless	18,488	165	[]
student	ok	18,488	166	[]
student	just wanna make sure '	18,488	167	[]
student	for rational equations	18,488	168	[]
student	you can solve x^2-1=0	18,488	169	[]
student	in denom	18,488	170	[]
student	cause last time i think i said wanst solvable	18,488	171	[]
student	/no domain	18,488	172	[]
volunteer	Yes you can	18,488	173	[]
student	ok	18,488	174	[]
volunteer	Is that all, or do you have any other questions?	18,488	175	[]
student	thats all	18,488	176	[]
volunteer	I'll end the session here. Have a nice day!	18,488	177	[]
volunteer	Hello!	18,534	0	[]

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