Question

h/h-1 - h-1/h = 1/12

Answer 1

\[\frac{h}{h-1} -\frac{h-1}{h} = -\frac{1}{12}\]ON the left side, find a common denominator.

Answer 2

What can that be? :)

Answer 3

idk

Answer 4

Well, we have \(h-1\) and \(h\)

Answer 5

h?

Answer 6

That can't be it, because how will we deal with the \(-1\)?

Answer 7

the easiest way to go about this is to multiply both of them together :)\[h(h-1)\]

Answer 8

you mean LCM?

Answer 9

Yeah. LCM, or common denominator, :P

Answer 10

h^2 - h^2 + 1 -2h?

Answer 11

over h^2 - h?

Answer 12

Let's see

Answer 13

Or..cross multiply.

Answer 14

Are you understanding what I am doing? :)

Answer 15

yes i am

Answer 16

I missed something actually.

Answer 17

If we multiply al the denominators together, our LCD would be \(12(h(h-1))\)

Answer 18

Now we have a common denominator. Sorry about that.

Answer 19

Do you see why? x_x

Answer 20

If we just multiplied \(h(h-1)\) with eachother, we could be neglecting he 12 on the other side of the equation, and we cannot do that if we are to evaluate for x.

Answer 21

we would*

Answer 22

what?

Answer 23

@ChiefArnav Which part have you gotten up to? Let's continue from there, step by step,

Answer 24

That way you can reference how I solved the problem and check your answer.

Answer 25

CarlosAgusta, please refrain from drawing or sending messages that are off-topic.

Answer 26

\[h/(h-1) - (h-1)/h = -1/12\]

So the first thing you want to do is get rid of the denominators, by multiplying everything by (h-1).

This leaves us with h - ((h-1)(h-1))/h = -(h-1)/12
Now we want to get rid of the h as a denominator, by multiplying everything by h, which leaves us with:

h^2 - (h-1)(h-1) = -h(h-1)/12

We can simplify this by h^2 - (h^2 -2h +1) = h(h-1)/12
All I have done there is multiply out the brackets
Simplify:

2h-1 = -h(h-1)/12

Times by 12:

24h-12 = -h(h-1)

Simplify:

24h-12 = -h^2 + h

rearrange:

0 = -h^2 - 23h +12

Use quadratic formula with
a= -1
b= -23
c= +12

I got two answers: 0.51 (approx) and -23.5

Hope this helps :D