Solving equations with rational expressions

#shorts #algebra

Solving equations with rational expressions. Common problem that I see on the SAT and ACT exams.

[davidseed]

another way.
reciprocal both sides
1-1/n= 1/3 ... get n on one side
1-1/3=1/n. .... simplify
2/3=1/n. .... reciprocal
3/2=n. answer

[Mipedazo]

dude keep it up, all the people who want it simple will miss out on the real workings of math. great content.

[oreosdilemma]

There's the best and easiest way to do this:

1 / 1 - 1/n = 3
Now we take the LCM in the denominator [Least Common Factor]

the least common factor in the denominator will be n.. therefore,

1/ 1 • n/ 1 • n- 1/n

which is
1 divided by n-1/n = 3
it can also be written as the reciprocal of it which would be

n/n-1 = 3
we take n - 1 to the other side and multiply it by 3

3n - 3 = n
we take n to the left and 3 to the right
3n - n = 3
2n = 3
n = 3/2

and as easy as that (6 steps)
overall steps without explanation:

1/1-1/n = 3

1/n-1/n = 3

n/n-1 = 3

3n - 3 = n

2n = 3

n = 3/2

[kwith]

I'd have just multiplied both sides by 1-1/n and went from there. Cancels the initial fraction and is easier to solve for n

[georgiamorris]

1/(1-1/n)=3
just multiple but 1-1/n 1=3(1-1/n)
Expand bracket 1=3-3/n
Minus 3 1-3=-3/n
Simplify 2=-3/n
Divide by n/2. 2(n/2) = -3/n (n/2)
Simplify. n= -3/2

[dadyasuo]

I set the denominator equal to 1/3 and therefore 1/n = 2/3 so n=3/2

[mylohiga]

heres what i did
1 - 1/n = 1/3
1/n = 2/3
n = 1.5

[russellmurray]

A fraction within a fraction . . . or as some may say, a complex fraction.

[Adnankhan-fdzr]

Here you learn how to complicate things

[훛훛]

What is was just to see that
1 1 1 2 1
- =1 and - =3 so - = - = -
1 1/3 n 3 1.5

n=1.5

[skill_issuesmo]

you can just think at the start, if i divide 1 by something that equals to 3 what would it be? you would get 1/3 and now the n would be obvious

[noice]

This is cool! The 1/n basically outputs a fraction, and then the output of the whole equation is the output of (1/n) + 1 That's neat.

[abhinavdwivedi]

Why to make it complicated, just take LCM in denominator and it becomes 1 by n-1/n i.e.n/n-1
Now move n-1 to other side to make 3n-3, just move the n to 3n and make 3 positive
You got 3/2

[lavi]

I would just multiply both sides by the denominator. Why do all this??

[leina_a]

Or you can just say that 1-1/n= 1/3
Then you just have a 2 steps resolve

[chrissystewart]

I'm ready for my lessons I never learn this in school

[za_k]

How come you don’t multiply the right side by n/n?

[joarschumacher]

Just one questions, I thought that you should multiply all terms with “n”? Why didn’t you multiply the right side by N

[jmaxim]

Too complicated. Would have worked on the denominator, inverted it and set equal to 3 then solve.

[akbarmirzo]

You can do scan equation with photomath and valya 😅