Question

Solve for x be sure to show ALL STEPS Please .
10 4 5
---------- + ------ = ---------
x(x-2) x x-2

Answer 1

The problem is

\[\Large \frac{10}{x(x-2)} + \frac{4}{x} = \frac{5}{x-2}\]

right?

Answer 2

Yes , Correct . @jim_thompson5910

Answer 3

ok before I attempt to solve, I should point out one thing

Answer 4

we CANNOT divide by zero

so each denominator CANNOT be zero

Answer 5

Oh okay . Got it !

Answer 6

so

x cannot equal 0

and

x-2 cannot equal 0 -----> x cannot equal 2

Answer 7

now let's solve

Answer 8

\[\Large \frac{10}{x(x-2)} + \frac{4}{x} = \frac{5}{x-2}\]


\[\Large \frac{10}{x(x-2)} + \frac{4(x-2)}{x(x-2)} = \frac{5x}{x(x-2)}\]


\[\Large \frac{10}{x(x-2)} + \frac{4x-8}{x(x-2)} = \frac{5x}{x(x-2)}\]


\[\Large \frac{10+4x-8}{x(x-2)} = \frac{5x}{x(x-2)}\]


\[\Large \frac{4x+2}{x(x-2)} = \frac{5x}{x(x-2)}\]


\[\Large 4x+2 = 5x\]


\[\Large 2 = 5x-4x\]


\[\Large 2 = x\]


\[\Large x = 2\]


So the only *possible* solution is x = 2


But wait...before I said that x cannot equal 2 (since this causes a division by zero error).


So this means that there are NO solutions

Answer 9

If you didn't know about this restriction, then checking the possible solution of x = 2 would have given you 0 in the denominator somewhere, which would lead you conclude that x = 2 is not a solution at all

so that check would show there are no solutions

Answer 10

Thank you for breaking it down . This really helped me because i have a couple more questions like this . And Okay now i understand . Thanks a MILLION ! :)

Answer 11

you're very welcome, glad it's starting to click

Answer 12

Do you know why you can never divide by 0?

Answer 13

Who ? Me ? @skullpatrol

Answer 14

Yes. @Forever_Me

Answer 15

@Forever_Me Would you like me to explain why?

Answer 16

Yes please ! @skullpatrol

Answer 17

Ok, but you have to ask questions if you don't understand something.

Answer 18

@Forever_Me will you do that?

Answer 19

one way to think of why you can't divide by zero

if you could divide by zero, then let's say x/0 = 0

multiply both sides by 0 to get x = 0*0 which leads to x = 0

Now say you let x = 3

x/0 = 0

3/0 = 0

3 = 0

which is impossible

-------------------------------------------------------

Now let's say x/0 = 1

x/0 = 1

x = 1*0

x = 0

but if x = 3 for instance, then you get yet another contradiction

so these contradictions are some examples of why division by zero is undefined

Answer 20

Okay @skullpatrol

Answer 21

I never really understand wh we couldnt divided by zero , So thanks for explaning to me (: @jim_thompson5910

Answer 22

Why*

Answer 23

sure thing

Answer 24

Let us start with what the reciprocal of a number means:

reciprocal: Two numbers whose product is 1, also called multiplicative inverses.

5 and 1/5 are reciprocals because 5*(1/5)=1

Answer 25

What is the reciprocal of 4/5 @Forever_Me ?

Answer 26

@Forever_Me What number times 4/5 equals 1?

Answer 27

Umm would it be : 5 ?

Answer 28

Does 5*(4/5) =?= 1

Answer 29

Remember the definition of a reciprocal...Two numbers whose product is 1

Answer 30

Does it have to be a single number (ex: 5,4,6,7 ) or can it be times by a fraction to get 1 ?

Answer 31

It can be any number you want.

Answer 32

So yes, it can be a fraction.

Answer 33

It does not have to be a single "digit" like 5,4,6,7

Answer 34

4/5 times 5/4 =1

Answer 35

Correct!!! Very GOOD :-D

Answer 36

:) Thankss !

Answer 37

What is the reciprocal of 6?

Answer 38

Remember: 5 and 1/5 are reciprocals because 5*(1/5)=1

Answer 39

1/6 TIMES 6 = 1

Answer 40

Yes! What is the reciprocal of 1000?

Answer 41

1000 times 1/1000 =1 .

Answer 42

Yes! So your answer to the question:
"What is the reciprocal of 1000?"
Should be 1/1000,
because 1000 times 1/1000 =1

Answer 43

@Forever_Me do you really understand this?

Answer 44

Honestly i really do . You broke it down to the point were i could really understand this . (:Thank you .

Answer 45

Ok, now comes the question:

What is the reciprocal of 0?

Answer 46

No solution ? Because 0=0 over 1 so the recipricol is 1 over 0 which is undefined. Right

Answer 47

What skullpatrol is saying is this

if p is the reciprocal of q, then

p times q = 1

-------------------------------------------------------

but

0 times any number = 0

any number times 0 = 0

so there's no way for

a*0 = 1

or

0*b = 1

to be true for any value of 'a' or 'b', which means that 0 has no reciprocal

Answer 48

Remember this

What number times 4/5 equals 1?

Here the question becomes

What number times 0 equals 1?

Answer 49

Similarly here:

So your answer to the question:
"What is the reciprocal of 1000?"
Should be 1/1000,
because 1000 times 1/1000 =1

Becomes
"What is the reciprocal of 0?"
Should be "no-number,"
because 0 times "no-number" =1