What is this Equation? Let’s learn the steps to solve it…

[@Kleermaker1000]

I did it as follows: Y + 2 = Y^2 => - Y^2 + Y + 2 = 0. Multiply everything by - 1 and you get: Y^2 - Y - 2 = 0. Factoring gives (Y - 2)(Y + 1) = 0 => Y = 2 and Y = - 1. Plug these values in the original equation and you get: 2/4 = 1/2 (correct) and - 1/1 = 1/ -1 (- 1 = -1), which is also correct. So the solutions are: Y = 2 and Y = -1.

[@johnbrandolini2915]

Just as you suspected I attempt to solve the problems in your videos before watching your solutions. My method for solving this problem turned out to be the same as yours. I am a retired EE but still get pleasure in solving math problems. Btw, I am 75. 😺

[@darellpiper7227]

I also am a retired EE and I enjoy working the math problems on You Tube.

[@johnbrandolini2915]

@@darellpiper7227 I’m also an amateur radio enthusiast, call N1ABE. The math comes in handy when designing filters and working with MMICs.

[@robertakerman3570]

@@johnbrandolini2915 Hi N1. Aren' t there charts or calculators 4 that?

[@johnbrandolini2915]

@@robertakerman3570 There are. Microwave Office is a common one. The copy I have is a bit out of date and I don't want to spend the bucks to upgrade. However, Excel is pretty good at plotting filter response once I derive the equation and set up the spreadsheet. Before I retired the company I worked for used Labview not only to control the test equipment but also to take the data and compute parameters such as return loss and 2nd order intercept. However, some stuff had to be calculated by hand so to speak. I got spoiled using Agilent's (now Keysight) PNA-X network analyzer and really wanted something similar to add to my workbench. Since then I acquired 2 pieces of gear, a nanoVNA (vector network analyzer) and a tinySA (spectrum analyzer) which performs a lot of the measurements I used to collect at work.

[@joebrinson5040]

@ John Brandolini, so am I, industrial engineer. ( Also KC1BR).

[@murdock5537]

Nice challenge, superb way to solve it, many thanks! Criss-crossing = fast lane solving the problem: y/(y + 2) = 1/y → y^2 = y + 2 → (y - 1/2)^2 = (3/2)^2 → y_1= 2 and y_2 = -1 😊

[@danieldennis9831]

LCD is y^2+y. but I also thought of flipping the equations upside down so the LCD became y. Cross multiplying still ends up with y^2=y+2. y^2-y-2=0. (y+1)(y-2)=0 y=-1,2. That checks.

[@jim2376]

Cross multiple. Everything to the left side. y^2 - y - 2 = 0. Factor. (y - 2)(y + 1) = 0. 2 or -1

[@tobyharnish8952]

1/y=(y+2)/y First, we will multiply everything by 'y' to cancel out the fractions. y+2=1 y+2-2=1-2 y=-1 So, this is the answer. Another way to do this is by factoring. First, we must multiply the fractions together. In this case, multiply 1 by (y+2) and y by y^2 You should get this: y+2=y^2 To solve, we must write this equation in standard form (ax^2+bx+c=0) Therefore, we have the following: y^2-y-2=0 Now, we could use the discriminant to determine how many solutions we have. But it is not really helpful to do this way. The next step is to ask yourself this question: "What multiplies to -2 but adds to -1?" Well, negative 2 times positive 1 is negative 2, and negative 2 plus 1 is -1. When you found these numbers, just put them inside parentheses. (y-2)(y+1)=0 If we set both equations equal to 0, we get y-2=0 y-2+2=0+2 y=2 y+1=0 y+1-1=0-1 y=-1 Now we must test out these solutions to make sure that they are indeed the correct one First, we can try -1 1/-1=(-1+2)/-1 -1=-1 TRUE Now, let us try 2 1/2=(2+2)/2 1/2=2 FALSE So -1 is the only solution

[@robertakerman3570]

Toby, I don't know enuf to follow UR comment, but it certainly sounds good.

[@murdock5537]

Your first equation is different to the equation of tablet class...🙂

[@ASChambers]

Nice simple step by step explanation :-)

[@chrisbrown865]

MUCH APPRECIATED

[@rpwdpm]

you made the solution to this problem much more difficult than it needed to be. the y in the numerator on the left side of the equation and the y on the denominator on the right side of the equation cancel each other out. so that leaves y+2=1. therefore y=1-2. so y=-1. easy peasy.

[@Kleermaker1000]

Not so "easy peasy" as you thought: there are two solutions: Y = 2 and Y = -1. Check it yourself. :)

[@genomeano]

Although it's a lot longer method, I used the quadratic formula and got the same answer.

[@carlhopkinson]

2. by inspection

[@GwenPidgeon]

I'm a high school social studies teacher, and I honestly have no desire to solve this problem. Thank you for doing the work for me.

[@lilberry6976]

Y=-1

[@tobyharnish8952]

It would be nice if you will read allowed your question before solving them.

[@robertakerman3570]

Toby, no offense- it's "aloud": it reads easier.

[@JDH___]

erm what the sigma

[@spudhead169]

Lol, I just looked at it for 2 seconds and said 2 & -1, it was obvious.

[@robertstack2144]

You are too gabby. I solved it in my head.