5

Solve each equation.$$ rac{n}{n+3}+5= rac{12}{n+3}$$...

Question

Solve each equation.$$ rac{n}{n+3}+5= rac{12}{n+3}$$

Solve each equation. $$ \frac{n}{n+3}+5=\frac{12}{n+3} $$



Answers

Solve each equation. $$ \frac{n}{n+3}+5=\frac{12}{n+3} $$

3/5 n 3/5 of some number is equal to negative three tents. All right, so when we're when we've got a variable being multiplied by a fraction and we want to get that variable by itself, the easiest way is actually to multiply by the reciprocal of that fraction, because then they end up with 15 over 15 times in 15 15. Send is one end, or you might look at his three over three is 15 over five is one, so we just end up with N So if we multiply by 5/3 on the left, we also have toe multiply by 5/3 on the right. I always like to try and simplify before I multiply. So I'm looking at like negative three over three is like negative one over one and five over 10 is like one over two. And then we can multiply numerator times. Numerator negative. One times one is negative. One denominator times denominator. Two times one is two. So our answer is negative. 1/2 3/5 of negative. 1/2 is negative. Three tents. Let's check that and make sure it's true. So we're gonna take 3/5 times and which we know to be negative. 1/2 or we think is negative. 1/2. We're gonna see if that equals negative. Three tents you see pretty quickly. It does three times negative. One is negative. 35 times two is 10. So negative. 3/10 equals negative. Three tents. That means our answer negative 1/2 is the correct answer.

We'll start by subtracting five and from both sides. So now the ends are on the same side. Thes cancel out. We have a negative 12 left over here. The re n minus five and this negative to m divide people sites by negative tube and em is equal to six.

So it does. One last times 24 on both sides will have 24 times on last 1/8 minus U minus and over three e close to 24 times 5/6. So three times and last one miners eight times to U minus and ik o seu four times. But by the distributive property, three end class three miners 16 plus eight equals to 20. So now we come by and luck term were how 11 on my nose certain you fell suit lunch so less I searching on post said Well, how you lavon Andi close to service tree and we divide both sides by 11 were how unequal shoe street.

Today, we're going to solve the following equation. End times two and minus three is equal to two. In order to do this, we're going to expand our bracket to get to end squared ministry and is equal to two. We're gonna take the two over to the other side to get to end squared minus three and minus two is equal to zero. Since the leading coefficient of n squared is not equaled one win it. Use an alternative method. We're gonna multiply coefficient of n squared onda out, uh, constant together. So you get two times minus two is equal to minus four. Also going to write down what beers minus three b in terms of X squared plus b x plus C go. Now we're looking for two numbers. Ah, let's choose Alfa and Beater Such that out for times beat is equal to minus four, but Alfa plus beater is equal to minus three. Now, in order to find such numbers, we'll just go through the factors of four to figure out how we could get this number since, uh, eight times beers, a negative number. We know that either a or B is negative, but not both can be. So four can be gotten by one times four. And in fact, one minus four is equal to minus three. So we found our combination, Since one times minus four is equal to minus 41 minus four is equal to minus three. Now we're going to rewrite, um, to end squared minus three and minus two as two and squared. Ah, minus four end plus and minus two from the 1st 2 were going to factor out to end to get n minus two on the next. We're just gonna fact try a one to get n minus two. Now, both terms have gotten them ones, too. Which would come fact around, then we're left with two n plus one, and this is all equal to Zahra. In doing this, we have found that either end minus two is equal to zero. Telling was, pen is equal to two or to end. Plus one is equal to zero. So to and is equal to minus one or end is included minus 1/2. And here are two solutions. Thank you.


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