Solving a rational equation with two solutions

👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rational expressions by the lowest common multiply (LCM) of the denominators. This eliminates the denominators and then we can evaluate the resulting equation accordingly.

It is very helpful to check your results by substituting them into the original equation to see if they are true. This also helps to identify the extraneous solutions. An extraneous solution is a solution that is obtained during the course of solving an equation but which does not hold true for the original equation.

Timestamps:
0:00 Intro
0:26 Start of Problem

Corrections:
5:16 It is positive 6x, not 2x.

Organized Videos:
✅ How to Solve Rational Equations
✅ How to Solve Rational Equations with Trinomials
✅ How to Solve Rational Equations with Binomials
✅ How to Solve Rational Equations with Monomials
✅ How to Solve Rational Equations with an Integer
✅ How to Solve Rational Equations | Learn About
✅ How to Solve Proportions with Binomials
✅ How to Solve Proportions with Trinomials

Connect with me:

#rationalfunctions #brianmclogan

[fernandadiaz]

i'm in college and still look to you when I don't understand my professor, awesome job, your students are very lucky to have you!

[alwaysnelsontacos]

Why he got to call out Danielle like that

[garycook]

I am a Dad trying to help his son understand solving rational equations. I am having to learn this all over again. This video was very helpful. Your students are lucky to have you. I will undoubtedly watch it a couple more times.

[novie]

Brian, I don't know if you read comments on old videos, but thanks to the pandemic, taking online classes has meant a lot of struggle. Currently I'm in a class that doesn't have much in the way of video supplementary material, and I can't tell you how much all your hard work has helped me passing my tests this quarter (even if it's by the skin of my teeth!)

[jamesh]

Well looks like I'm failing tommorow

[truthobservatory]

Holy shit i figured it out god bless you

[jennifersmith-colton]

Holy hell. I've been stuck on this one concept and FINALLY, a video I can follow 😅😅.

[dahlia]

The best math teacher award must goes to you 🥺 Thank you for helping!

[rubyanngarcia]

It's really great to have this video shared, I was able to help my brother with his assignments even though I've graduated from this
a very long time ago. Wish I had this back then when I was in college! T.T Students are now lucky to have this tutorial available online.

[Yirukai]

Preparing for the GMAT. These videos are pure gold to me. Thank you so much Brian.

[behzadramandi]

@Brian McLogan Thanks for the video, Sir, but the correct answers for X are X= -2 and X=3/2. If you go back to your video you'll see where the mistake comes from. Right after factorization when you broke the equation into two parentheses the correct form should be (2X-3)(X+2) but you put it as (2X+3)(X-2). In other words, the way you put it we would have 7X and not (-1)X. Thank you!

[roxyqueen]

Great !!! TEACHER!!!! I wish I had you when I was coming up in my high school years..all my teacher did was sleep or read my freshman year..seriously u r truly awesome!!

[mr.toffee]

8:07 Wait hold on, that should be - 3 & + 2, because if you add 3 and - 2, that would be + x, but given the - x, the greater number should be negative, which is - 3….

[juhbulis]

2:46 was a jump scare dude I thought I was getting taught math not pooping my pants

[UrtleMnL]

Wow, this is super useful! Even though I'm not in your class, I get a whole explanation of everything as if I was there!

[ldsspbu]

I am a student and this is in my final When you multiply numerator you also multiply the denominator so what are you doing can you explain

[Natasha-thbb]

Thank you so much! Your teaching is great :)

[JosiahHenry]

Isn’t it crazy how this video is still of use? Thank you so much! Big test coming up tomorrow!

[som_girl]

one is also a denominator that should have been among the LCD products. It's easier for anyone learning to find LCD to know that no denominator should be eliminated until they fully understand that one multiplied by any number is that number and can be ignored when finding LCD if it is a denominator. Great video!

[johnnolen]

Mr. McLogan, I recently became ensconced in a flame war over a comment I made on one of your videos over six months ago. In the meantime I have been inundated with recommendations for tutorials on how to solve rational equations, as if I needed the help.
Not to take anything away from your teaching, the method that you demonstrate here is entirely correct. Nevertheless, there is a more efficient way to solve such problems. If you have a proportion (a rational equation) of the form a/b = c/d then a*d = b*c. This is true because multiplying the original proportion by b*d on both sides of the equals sign such as b*d*a/b = c/d*b*d, yields a*d = b*c; this result is always true. Hence for the equation in question: 6x/(x+4) + 4 = (2x+2)/(x-1), we can first find a common denominator for the terms on the left hand side: [6x + 4(x+4)]/(x+4) = (10x + 16)/(x + 4). Substituting this expression for the original left hand side we obtain, (10x+16)/(x+4) = (2x+2)/(x-1). The foregoing theorem guarantees that (10x+16)(x-1) = (2x+2)(x+4). FOILing both sides gives 10x^2 +6x -16 = 2x^2 +10x +8. Moving all terms to the LHS, 8x^2 -4x -24 = 0. Factoring this quadratic equation gives 4*(x-2)*(2x+3) = 0. This yields the solution set {-3/2, 2}, the same as your method.