Question

simplify: (1/x + 1) / (1/x - 1)

Answer 1

Is this the question:

\(\cfrac{\cfrac{1}{x} + 1}{\cfrac{1}{x} - 1}\)

Answer 2

yes

Answer 3

Good now if x is not 0, then I can take x as LCM in both numerator and denominator. What will you get ?

Answer 4

um I'm not quite sure

Answer 5

Ok let me help u there:

\(\cfrac{\cfrac{1+x}{x}}{\cfrac{1-x}{x}}\)

Answer 6

would you cancel out the x's?

Answer 7

Yes great. Now tell me what will you get?

Answer 8

[1+x \div 1-x\]

Answer 9

Very nice.

Answer 10

Now that's your answer.

Answer 11

Thank you!

Answer 12

Brilliant work and keep it up. Try to understand the basic concepts and you will clear every examination with flying colours.

Bye and enjoy your time at OS.
Gud day !

Answer 13

How do you find the inverse of an equation?

Answer 14

Well actually you have to understand that inverse has various meanings in various contexts. So, you will have to specify it. Try to give me an example and I will help you out. :)

Answer 15

\[f(x) = \frac{ 2x-3 }{ 5 }\]

Answer 16

Ok:

See actually the best way to solve such type of question is this:

(1) put f(x) = y
(2) Find value of x in terms of y
(3) Replace y by x and x by y.

Answer 17

See:

(1) f(x) = y = (2x-3)/5

(2) Find value of x in terms of y:

5y = 2x-3
=> 5y+3 = 2x
=> x = (5y+3)/2

(3) replace x by y and y by x

So you get
y = (5x+3)/2
Now put this y = g(x)

So, g(x) = (5x+3)/2

Now, this g(x) will be the inverse function of f(x).

Answer 18

Did you get it?

Answer 19

Yes thank you so much again!

Answer 20

Hey there is no problem.

It was my pleasure.

Answer 21

if an absolute value decreases doesn't the graph narrow?

Answer 22

Lets find out with the help of a graph:

Lets say :

|x| was initially 2 then it became less than 2. Okay ?

Answer 23

Okay!

Answer 24

Now lets see its graph:

Initially:


Finally:


(sorry couldn't shade it properly)

Now the equation |x| < 2 signifies all values of x such that -2<x<2.

So, we cannot say about narrowing of graph.