Problem

Solve each equation. Check your solutions. $$ 1+\…

Problem 19 Easy Difficulty

Solve each equation. Check your solutions.
$$
3=\frac{1}{t+2}+\frac{2}{(t+2)}
$$

Answer

$\left\{-\frac{8}{3},-1\right\}$

Related Courses

Precalculus

Algebra

Beginning and Intermediate Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 4

Equations Quadratic in Form

Discussion

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Video Transcript

because we have three is equal to one over T plus two minus two over t plus two square or C. Ok, so we multiply. Um, well, I'm through by the out CD of T plus two square. So I guess it's worth noting here. Right, that t plus two, though. T plus two kidnapping equal 20 right? Because, well, our glamorous because secretly also depressed it can't be good deal. Okay, but we're gonna move by through by Well, by t plus two squared. So we have t plus two squared. Okay, um, Times three. Kym Street is equal to about T plus two squared times the right side of the equation. So time was one over T plus two plus two over people's to square. Okay. And we get here is when we get the t plus two, um, square times three. So we get three times or t plus two square is t square class for tea. Plus four is equal to Well, this just becomes, um, well, t plus tour cause too. Okay, so we get Well, we disagree. Here. We get three t square. Um, cost 12 to you, cause 12 Okay is equal to? Well, t plus two plus two or people's four. Right? And then, um, while we go ahead and we set our equation equal to zero. So where we get we get three t square, and then we have 12 tm minus t plus 11 uh, t. And then we have what? Plus eight because plus 12 miles fork. So, um, conceits right is equal to that zero. Now we have our equation a quadratic equation in standard form, which doesn't look like a factor. Too nice. You can go ahead and we can use the quadratic equation, right? Yes, we have that. In this case, T is equal to or negative be customers swear it of B squared minus four a. C o on the bottom I to wait right where a is three feet 11 and C is eight. So we get that tea is equal to or native be some negative 11 plus or minus the square root of 11 square minus four times a just three times. See, which is it's all the right it by two times a day or two times three. Okay, so therefore, t is equal to this becomes while in negative 11. Um, plus or a minus. This is the square root of 25. This is Disposer minus phi over, Um, over three times to over six. Okay, so what we get here, we get that while our solutions are either negative one. So this is equal to either, um, negative one or negative eat thirds. Okay, Now we have to go in and check. So I would into our original equation right here. Go ahead and plug in native one, and then negative 1/3 and you'll see that the right side in both cases device to 3 to 3 to three. You plug it into either maple or well from Alfa would probably you don't probably good what you could do by hand, but either where you're going to see that, um, both in quick solutions to work. So therefore, our solution sets is well, the sets containing thes two points of the second tending to one and negative 8/3. What

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