Solving Rational Equation with Whole Number - Part 2 - General Mathematics
Summary
TLDRIn this educational video, Ton teaches viewers how to solve rational equations with whole numbers. He starts by identifying the least common denominator (LCD) and restricted value (RV), which is crucial to avoid undefined expressions. The LCD in this case is x-5. He then demonstrates the process of eliminating the denominator by multiplying the entire equation by the LCD, leading to a simplified equation. After solving, he finds x=15, and checks the solution by substituting back into the original equation. The video concludes with a reminder to like, subscribe, and turn on notifications for more informative content.
Takeaways
- 📘 The video focuses on solving rational equations, specifically one involving a whole number.
- 🔍 The key to solving rational equations is eliminating the denominator.
- 🌟 The LCD (Least Common Denominator) for the given equation is (x - 5).
- ⚠️ The Restricted Value (RV) is x = 5, as this makes the denominator zero, resulting in an undefined expression.
- 📖 The process involves multiplying the entire equation by the LCD to eliminate the denominators.
- 🔢 After multiplying, the equation simplifies to 3x = 5x - 25.
- 🧮 Transposing terms leads to 2x = 30, which simplifies to x = 15.
- 📝 The solution set is x = 15, which is the value that satisfies the original equation.
- 🔄 To verify the solution, substitute x = 15 back into the original equation and check for equality on both sides.
- 📢 The presenter encourages viewers to like, subscribe, and turn on notifications for updates.
Q & A
What is the main topic of the video?
-The main topic of the video is solving rational equations, specifically focusing on how to eliminate the denominator in a rational equation.
What is the given rational equation in the video?
-The given rational equation is \(\frac{3x}{x-5} = \frac{5}{x-5}\).
What is the LCD (Least Common Denominator) for the equation presented?
-The LCD for the given equation is \(x-5\), as it is the common denominator present in both fractions.
What is a Restricted Value (RV) in the context of the video?
-A Restricted Value (RV) is a value that makes the denominator of a fraction equal to zero, which would make the fraction undefined. In this case, the RV is 5 because \(x-5 = 0\) when \(x = 5\).
How does the video suggest eliminating the denominator?
-The video suggests eliminating the denominator by multiplying the entire equation by the LCD, which is \(x-5\) in this case.
What is the simplified form of the numerator after eliminating the denominator?
-After eliminating the denominator, the numerator simplifies to \(3x\) on the left side and \(5x - 25\) on the right side.
How is the value of x found in the video?
-The value of x is found by simplifying the equation to \(3x = 5x - 25\), then isolating x by subtracting \(3x\) from both sides to get \(2x = 30\), and finally dividing by 2 to find \(x = 15\).
What is the solution set for the rational equation according to the video?
-The solution set for the rational equation is \(x = 15\).
How does the video suggest checking the solution?
-The video suggests checking the solution by substituting \(x = 15\) back into the original equation to see if both sides are equal.
What is the result of checking the solution in the video?
-Upon checking, the video confirms that substituting \(x = 15\) into the original equation results in both sides being equal, verifying that the solution is correct.
What is the final advice given by the presenter at the end of the video?
-The presenter advises viewers who are new to the channel to like, subscribe, and enable notifications to stay updated with the latest uploads.
Outlines
📘 Introduction to Solving Rational Equations
The speaker, Ton, introduces the topic of solving rational equations with a specific example provided by a subscriber. The equation given is 3x/(x-5) = (5-5)/(x-5). Ton emphasizes the importance of eliminating the denominator to solve the equation. The LCD (Least Common Denominator) is identified as x-5, and the restricted value (RV), where the denominator becomes zero, is also x-5. The process involves multiplying the entire equation by the LCD to eliminate the denominator, resulting in a simplified equation of 3x = 5x - 25. The solution to the equation is found by isolating x, which gives x = 15 after dividing both sides by 2.
🔍 Verifying the Solution to the Rational Equation
Ton demonstrates how to verify the solution to the rational equation by substituting x = 15 back into the original equation. The left side of the equation simplifies to 45/10, and the right side also simplifies to 45/10, confirming that the solution x = 15 is correct. Ton concludes the video by encouraging viewers to like, subscribe, and turn on notifications for updates. He signs off with a friendly farewell.
Mindmap
Keywords
💡Rational Equation
💡LCD (Least Common Denominator)
💡Restricted Value
💡Eliminate the Denominator
💡Numerator
💡Transposing
💡Simplifying
💡Solution Set
💡Checking
💡Undefined
Highlights
Introduction to solving rational equations with whole numbers.
Explanation of a rational equation given by the equation 3x/(x-5) = 5 - 5/(x-5).
Emphasis on eliminating the denominator in rational equations.
Identification of the LCD (Least Common Denominator) as x-5.
Definition and calculation of the Restricted Value (RV).
Explanation of why a fraction with a zero denominator is undefined.
Process of multiplying the entire equation by the LCD to eliminate the denominator.
Simplification of the equation after eliminating the denominator.
Isolation of the variable x by transposing terms.
Solving for x to find the value of x = 15.
Introduction to the solution set notation SS = 15.
Explanation of how to check the solution by substituting x back into the original equation.
Verification that the solution x = 15 satisfies the original equation.
Encouragement for viewers to like, subscribe, and use the bell button for updates.
Conclusion and sign-off by the presenter, Ton.
Transcripts
hi guys it's me ton in our today's video
we will talk about another part of
solving rational equation so we have
here 3x overx - 5 is equal to 5 - 5 /x -
5 so without further Ado let's do this
topic so let's solve this problem what
we have here is a rational equation
wherein actually this one is a requested
topic or video from one of our
subscribers video solving rational
equations with whole number so here it
is now guys the very important thing
here in solving rational equations is on
how to eliminate this
denominator first we need to know what
is your
LCD so as you can see here in this given
rational equation they'll C this simply
x - 5 because only have x - 5 we have
here invisible one as your
denominator
and we also have here another x - 5 so
in other words your LCD is simply x - 5
then after that we also need to
know your restricted value so so many of
us many of our viewers are asking what
is RV so it is
restricted
value so how do we calculate for the
restricted
value
guys it will become zero and here the
restricted value or
RV is simply from
because if you will plug in five here
and here your denominator will become
zero and
remember fraction with zero denominator
automatic that is
undefined okay so we are done with the
LCD and restricted value now let's use
the LCD to eliminate this denominator by
simply multiplying your whole equation
by x - 5
and x - 5 when I say whole equation and
close your equation parenthesis or
bracket and then multiply it both
sides here it will become this one we
have
3x
time x -
5
over x - 5 is equal to 5 5 then this
multiply here to your whole number it
will become 5
* x - 5 and here we have
minus multiply it here - 5 * x - 5 over
x - 5 so as you can see in
our numerator we have x - 5 x - 5 oh
sorry
okay so here as you can see we can
easily eliminate your
denominator and here your numerator so
it will become simply 3x okay then equal
to here which
is
5 5 *
X which is 5X then 5 * -5 that is -25 or
- 25 5 and here guys let's cancel
out 5 x - 5 and x - 5 we have - 5 so we
will simplify this equation it will
become
3x is = to
5x and this one
is3 so what will happen here is that I
would transpose 3x to the other side and
I will transpose -3 to the other side
so I will copy
5x the very reason
3x negative okay so 3x -3x then 30
postive 30 so 5x - 3x is simply 2x is
equal to 30 and to simplify and to
finally solve for the value of x what
you need to do is divide both sides of
the equation by two and and here it is
your X is equal to 15 and this is the
value of x here again this is the value
of x you can write down your answer as
solution set we have SS or solution set
be equal to this one
15 yeah now if you want to check whether
your answer is correct you can know you
can do a checking okay
checking so what will happen is that
using this original equation
we will substitute 15 to X so it will
become 3 * 15 okay 3 * 15 over 15 - 5 so
this is your X it will become
15 is equal to 5 okay 5 - 5 I'm copying
the original equation over this is 15 -
5
simplify 3 * 15 is 45
over this is 10 -
5 equal to 5
- 5 over
10 so as you can see this five can be
expressed as
50 / 10 - 5/
10 is = to 45 over 10 and what we have
here let me adjust
this one this is 45 / 10 and 50 10 - 5/
10 is simply 45 over 10 as you can see
the two sides of the equation upon
checking is are equal meaning the
variable X which is equal to 15 is
correct in the given equation 3x - 5 is
= to 5 - 5 over x - 5 so I hope guys you
learned something from this video on how
to solve for a rational equation with a
whole number so if you're new to my
channel don't forget to like And
subscribe but Bell button for you to be
updated latest uploads again it's me to
Chon byebye
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