What am i doing wrong?

B

bobisaka

Junior Member
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Dec 25, 2019
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Now, how do i get the answer of -1,-2?.. that would mean i should have an factored expression of (x-1)(x-2) = x^2-2x-x-2 = x^2-3x-2
I keep getting stuck

1. 2/x+5 - 1/x+1 = 1

2. (x+5)(x-5)2/x+5 - (x+5)(x-5)1/x-1 = (x+5)(x-5) 1

3. 2x-1-x+5 = x^2=x+5x-5

4. x+3 = x^2+4x-5

5. x+3-3 = x^2+4x-5-3

6. x = x^2+4x-8

Alternative answer:

6. x-x = x^2+4x-8-x

7. 0 = x^2+3x-8
 
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IF the equation is 2/(x+5) - 1/(x+1) = 1
With x= -1 the second fraction is not even defined! With x= -2, this is 2/(-2+ 5)- 1/(-2+ 1)= 2/3+ 1= 5/3, not 1 so neither -1 nor -2 is a solution.

To get rid of the fractions you should multiply by (x+ 5)(x+ 1) to get
2(x+ 1)- (x+ 5)= (x+ 5)(x+ 1)

2x+ 2- x- 5= x- 3= x^2+ 6x+ 5

x^2+ 5x+ 8= 0
Completing the square,

x^2+ 5x+ 25/4= -8+ 25/4= (-32+ 25)/4= -7/4
(x+ 5/4)^2= -7/4

That has no real solutions.

If the problem is actually (2/x)+ 5- (1/x)+ 1= 1 then 1/x= -5 so that x= -1/5. Again, neither -1 nor -2 is a solution. Where did you get the idea that they were solutions?
 
For it is written in the textbook answer as -1, -2..

I dunno, I am lost. I have gotten through the previous related questions fine. I will come back to it. Thanks.
 
I think the answer to "what am I doing wrong?" is "just about everything, starting with quoting the problem!"

I suspect the real problem may be [MATH]\frac{2}{x+5} - \frac{1}{x-1} = 1[/MATH].

Try solving that, and show us your work again, checking every line for errors and typos.
 
bobisaka said:
For it is written in the textbook answer as -1, -2..

I dunno, I am lost. I have gotten through the previous related questions fine. I will come back to it. Thanks.
Click to expand...
For the record if the solutions are x=-1 and x=-2 you should have (x+1)(x+2) NOT (x-1)(x-2)
 
Dr.Peterson said:
I think the answer to "what am I doing wrong?" is "just about everything, starting with quoting the problem!"

I suspect the real problem may be [MATH]\frac{2}{x+5} - \frac{1}{x-1} = 1[/MATH].

Try solving that, and show us your work again, checking every line for errors and typos.
Click to expand...
You are correct.

I have redone it three times, fixed the typos; i still come to the answer of (x+2) (x+1).. Textbook answer is (x-2)(x-1)..

1. 2/(x+5) - 1/(x-1) = 1

2. (x+5)(x-1)*2/(x+5) - (x+5)(x-1)*1/(x-1) = (x+5)(x-1)*1

3. 2x-2-x-5 = x^2-x+5x-5

4. x-7 = x^2+4x-5

5. x = x^2+4x+2

6. 0 = x^2+3x+2

7. (x+2)(x+1) = 0
 
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bobisaka said:
You are correct.

I have redone it three times, however i still come to the answer of (x+2) (x+1).. I have Textbook answer is (x-2)(x-1)..

1. 2/(x+5) - 1/(x-1) = 1

2. (x+5)(x-5)*2/(x+5) - (x+5)(x-5)*1/(x-1) = (x+5)(x-5)*1

3. 2x-2-x-5 = x^2-x+5x-5

4. x-7 = x^2+4x-5

5. x = x^2+4x+2

6. 0 = x^2+3x+2

7. (x+2)(x+1)
Click to expand...
But you got (x+2)(x+1) = 0, whose solution is x = -2 or -1, which is just what you said it was supposed to be!

Are you forgetting to do the last step, solving x + 2 = 0 and x + 1 = 0?

Also, there are still typos in what you wrote, which makes it hard for us to call you correct. Here is what you surely meant:

1. 2/(x+5) - 1/(x-1) = 1​
2. (x+5)(x-1)*2/(x+5) - (x+5)(x-1)*1/(x-1) = (x+5)(x-1)*1​
3. 2x-2-x-5 = x^2-x+5x-5​
4. x-7 = x^2+4x-5​
5. x = x^2+4x+2​
6. 0 = x^2+3x+2​
7. 0 = (x+2)(x+1)​

Right?

Also, you seem to be forgetting to check your answer, which would help to confirm it. If you said the answer was x = 1, 2, you would find that they fail; but if you finished the work and got x = -1, -2, you would find they satisfy the equation. (In fact, that's how I determined that my equation was the one you meant.)
 
You are correct in the typos, i redited them.

I did not finish the equation with x= -1, -2.
So, are you saying x= -1, -2 they hold the same value as x= +1, +2??
Sorry, I am confused, could you elaborate it you can on how i would get the answer of x=-1, -2.


Dr.Peterson said:
But you got (x+2)(x+1) = 0, whose solution is x = -2 or -1, which is just what you said it was supposed to be!

Are you forgetting to do the last step, solving x + 2 = 0 and x + 1 = 0?

Also, there are still typos in what you wrote, which makes it hard for us to call you correct. Here is what you surely meant:

1. 2/(x+5) - 1/(x-1) = 1​
2. (x+5)(x-1)*2/(x+5) - (x+5)(x-1)*1/(x-1) = (x+5)(x-1)*1​
3. 2x-2-x-5 = x^2-x+5x-5​
4. x-7 = x^2+4x-5​
5. x = x^2+4x+2​
6. 0 = x^2+3x+2​
7. 0 = (x+2)(x+1)​

Right?

Also, you seem to be forgetting to check your answer, which would help to confirm it. If you said the answer was x = 1, 2, you would find that they fail; but if you finished the work and got x = -1, -2, you would find they satisfy the equation. (In fact, that's how I determined that my equation was the one you meant.)
Click to expand...
 
bobisaka said:
You are correct in the typos, i redited them.

I did not finish the equation with x= -1, -2.
So, are you saying x= -1, -2 they hold the same value as x= +1, +2??
Sorry, I am confused, could you elaborate it you can on how i would get the answer of x=-1, -2.
Click to expand...
Can you continue solving it after your step 7? Did you follow a few examples? If a product equals 0 it means what?
 
lev888 said:
Can you continue solving it after your step 7? Did you follow a few examples? If a product equals 0 it means what?
Click to expand...
Ah i see, yes. I have used -2 to solve the equation and it becomes a positive. Okay, i believe i understand now.

2/(-2+5) - 1/(-2-1)

2/3 - 1/-3

2/3 + 1/3

3/3 = 1


Thanks guys, helped me alot.
 
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No no no no no! 1 and -1 are NOT equal. 2 and -2 are NOT equal. NO!

If you have (x+1)(x+2)= 0 then either (x+1) = 0 or (x+2) =0.


Lets look at x+1 = 0. If you plug in 1 for x you get that 1+1 = 0. Now you know that is wrong. So x can not be 1. Maybe we don't know what x is but it certainly is not 1. Can you think of a number that when you add 1 to gives you 0??

x+2 = 0. The solution for x can not be 2 simply because 2+2 is not 0. As simple as that. So what can x equal. Which number when you add 2 to it gives you 0 (remember that number is NOT 2)?
 
bobisaka said:
Ah i see, yes. I have used -2 to solve the equation and it becomes a positive. Okay, i believe i understand now.

2/(-1+5) - 1/(-2-1)

2/3 - 1/-3

2/3 + 1/3

3/3 = 1


Thanks guys, helped me alot.
Click to expand...
No, you have it wrong. 1st of all -1 + 5 is NOT 3. -1+5=4.

2ndly, you have to replace ALL the x's with the SAME x-value in the equation to check your answer. So first you check with x=1, see if that works and then you check with x=-2 and see if it works.

I'll show you what I mean by checking x=-2 for you.

2/(x+5) - 1/(x+1) = 1

2/(-2+5) - 1/(-2+1) = 1

2/3 - -1 =1
2/3 +1 =1
1 2/3 = 1 NO. So x=-2 is wrong.
 
Jomo said:
No no no no no! 1 and -1 are NOT equal. 2 and -2 are NOT equal. NO!

If you have (x+1)(x+2)= 0 then either (x+1) = 0 or (x+2) =0.


Lets look at x+1 = 0. If you plug in 1 for x you get that 1+1 = 0. Now you know that is wrong. So x can not be 1. Maybe we don't know what x is but it certainly is not 1. Can you think of a number that when you add 1 to gives you 0??

x+2 = 0. The solution for x can not be 2 simply because 2+2 is not 0. As simple as that. So what can x equal. Which number when you add 2 to it gives you 0 (remember that number is NOT 2)?
Click to expand...

I have redone it correctly. That piece of information helped me see the logic of that last step. Thank you!
 
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