SAT Math Part 3 - Solving Rational Equations and Factoring Trinomials - Free Educational videos for Students in K-12

SAT Math Part 3 - Solving Rational Equations and Factoring Trinomials - By The Organic Chemistry Tutor

Transcript


00:0-1	number 14 . Which of the following ? Could be
00:03	a value of X . So we have a rational
00:07	equation . 10 over X minus two is equal to
00:10	X plus one . How can we calculate the value
00:14	of X ? Well what I recommend doing is getting
00:19	rid of the fraction . So let's multiply everything by
00:23	X . So 10 over X times X . The
00:27	X variables will cancel Given us just 10 X times
00:33	negative two is negative two X . And then X
00:37	times X is X squared X Times one is X
00:41	. So this is what we have . Now let's
00:44	take everything from the left side and move it to
00:47	the right side . As we move -2 x to
00:51	the right side , it's going to change from negative
00:54	two X To positive two x . And as we
00:59	move positive 10 from the left to the right side
01:02	it's gonna become negative 10 . So this is what
01:05	we have now let's go ahead and combine like terms
01:10	. So we have X Plus two X which is
01:13	Drea Acts and thus we have X squared plus two
01:17	, reaction minus 10 . So now we have a
01:23	try no meal with the lien coefficient of one .
01:26	So let's go ahead and factor that expression . So
01:29	what two numbers multiply 2 -10 But add to positive
01:34	three . So we know five and 2 Will give
01:40	us 10 . If we multiply the two numbers now
01:43	, should we make The five negative or the two
01:46	negative -2 Plus five is positive three . So the
01:51	two has to be negative . Does two factor it
01:54	? It's going to be X plus five And X
01:58	-2 . So let's set each factor equal to zero
02:07	, Subtracting five from both sides . We get the
02:11	first solution . Acts is equal to negative five and
02:15	for the other one adding tunable sites gives us The
02:19	other answer acts as equal to two . Now this
02:24	answer is not listed . So A is the correct
02:28	answer . Choice acts is equal to negative five ,
02:32	number 15 . Which of the following could be a
02:36	value of X . And the equation shown below .
02:40	So here we have two fractions separate by an equal
02:43	sign . But with many try no meals . So
02:47	let's factor let's begin by factor in the first expression
02:51	X squared minus two X minus 24 . So let's
02:56	look for two numbers that multiply to negative 24 but
03:00	add to negative two . So this is gonna be
03:04	negative six and positive for So I'm going to buy
03:08	the as X -6 Times X-plus four . Now ,
03:13	what about the tree ? No mia on the bottom
03:15	left . So what ? two numbers Multiply 2 ,
03:19	12 . But at 2 , 7 Factors of 12
03:23	are one in 12 , two and 6 , three
03:26	and 4 . But 3-plus 4 adds up to seven
03:30	. So it's going to be X plus tree times
03:34	X plus four . Now , for the last one
03:39	on the bottom , right ? Two numbers that multiply
03:41	to negative six but adds a positive one . It
03:44	would be positive three A negative too . So we
03:48	have X plus two eight times X minus two .
03:55	Now , before we move on to our next step
03:58	, it's important to understand that We cannot have a
04:01	zero in the denominator . So the X values that
04:06	would produce zero and the denominator would make the function
04:09	undefined . So because we have the X plus three
04:12	factor on the bottom , X cannot equal -3 .
04:17	Here we have X plus four , so X cannot
04:20	be negative for and here we have X -2 .
04:24	So X cannot equal to -4 is one of the
04:29	answer choices . Since it would make The expression or
04:33	the function under fine . We can eliminate negative four
04:37	as an answer choice . So now what we can
04:43	do at this point is cancelled , we can cancel
04:45	X-plus four . And if we multiply the right side
04:50	and the left side by X plus story , we
04:53	could cancel the explanatory factors . So what we have
05:01	left over which I'm gonna right at the top ,
05:07	We have X -6 on the right side , I
05:09	mean on the left side and on the right side
05:11	we have 12 Over X -2 . So what do
05:17	you think we need to do at this point in
05:18	order to solve the equation ? What is our next
05:21	step ? Now let's write X -6/1 . So now
05:27	we have two fractions separated by an equal sign .
05:31	So we can cross multiply . So we're going to
05:34	have one times 12 which is 12 . And then
05:37	we're going to multiply X -6 by X -2 .
05:42	Our next step is to foil . So we're gonna
05:47	multiply X by X which is X squared . And
05:51	then x times negative two And the -6 times x
05:55	. And then negative six times negative two , which
05:57	is positive 12 . Now subtract in both sides by
06:03	12 . We're going to have zero is equal to
06:07	X squared And then we can combine these 2 -2
06:11	. X -6 . X is negative attacks . Our
06:16	next step is to factor the G C . F
06:18	. The greatest common factor , which in this case
06:21	is going to be X . So we can factor
06:24	this expression as x times X -8 . Now ,
06:30	what we're going to do is set each factor equal
06:31	to zero . So we have X is equal to
06:34	zero . And if you set X -8 equal to
06:37	zero When you saw that , you'll get access equal
06:39	to eight . Now zero is not one of the
06:42	solutions , but eight is , so E is the
06:46	correct answer choice for this problem .

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