Question

Solve the equation by the method of your choice.
Click to see problem

Answer 1

Where's the problem?

Answer 2

\[\frac{ 1 }{ x+13 }+\frac{ 1 }{ x }=\frac{ 1}{ 14 }\]

Answer 3

ok so i got x^2-5x+182=0

Answer 4

Whenever you have an equation containing fractions, first factor each numerator and denominator completely and then simplify each fraction by dividing like factors. Next multiply both sides by LCD (least common multiple of the denominators).

Are any numerators or denominators factorable in your problem?

Answer 5

wait thats 15x not 5

Answer 6

yes x+13 and 14x

Answer 7

14(x+13)+14x=x(x+13)

Answer 8

No! How are they factorable?

Answer 9

well you factor them out on top

Answer 10

No! You have the wrong idea about what I mean by factorable. Observe each numerator and denominator, individually. I never said multiply them. That's not factoring.

Answer 11

The answer is no, no numerators or denominators can be factored. OK so then the next question is, what is the LCD of the denominators? Can you tell me?

Answer 12

LCD is 14x(x + 13). Do you understand?

Answer 13

thats what i had

Answer 14

Right but that is LCD. That's not factoring each numerator and denominator. You must have a proper understanding of the vocabulary in mathematics.

OK so the next logical step is to multiply both sides by 14x(x + 13). So what do you get?

Answer 15

14x^2+182x

Answer 16

No. Multiply each term individually on both sides by 14x(x + 13). What do you get?

Answer 17

i dont understand

Answer 18

OK let's do this in baby steps. What do you get when you multiply the first term (the first fraction) on the left side of the equation by 14x(x + 13)?

Answer 19

14x+182+14x=x^2+13x

Answer 20

or 14(x+13)+14x

Answer 21

\[14x(x +13)(\frac{ 1 }{ x +13 })\]=?

Answer 22

14x?

Answer 23

im sorry its been a long day and i am just not getting it tonight

Answer 24

Right! Now what do you get when you multiply the second fraction on the left side by 14x(x + 13). In other words,\[14x(x +13) \frac{ 1 }{ x }\]= ?

Answer 25

14(x+13)

Answer 26

so is the -x^2+15x+182=0

Answer 27

Correct! Therefore the expression on the left side is\[14x +14(x +3)\]RIGHT?!

Answer 28

yeah so we do -b+-\[-15+-\sqrt{15^2-4(-1)(182)}/2(-1)\]

Answer 29

Not yet! Baby steps, remember? Now what do you get when you multiply the fraction on the right side by 14x(x + 13). In other words,\[14x(x +13)(\frac{ 1 }{ 14 })\]= ?

Answer 30

sorry x(x+13)

Answer 31

Correct! Thus we have the simplified equation\[14x +14(x +13)=x(x +13)\]Agree or disagree?

Answer 32

14x(x+13)+14x=x(x+13)

Answer 33

oh ok

Answer 34

Which is correct, mine or yours? What's the difference and do you spot the error?

Answer 35

yours you14x(x+13) not 14x just 14

Answer 36

Excellent! OK so now simplify the left side and the right side individually and right the simplified equation for me. Can you do that please?

Answer 37

*write not right. Sorry for the grammatical error.

Answer 38

14x+182=x^2+13x

Answer 39

-x^2+x+182=0

Answer 40

No, there seems to be a term missing on the left side when you simplified. Can you spot the error?

Answer 41

thats ok i didnt even notice way to sleepy to read right

Answer 42

i know hold on

Answer 43

28x+182=x^2+13x

Answer 44

It's not good, not having enough sleep. You should get at least seven or eight hours of sleep per night.

Answer 45

i try but midterms are coming up and i have to study

Answer 46

I love and appreciate your dedication to your education, however writing an exam tired won't help.

Yes! Alright now always try to keep the leading term positive. Since the quadratic term is positive on the right side of the equation, manipulate all terms to the right side. Thus the left side will be zero. Can you do that?

Answer 47

0=x^2+13x-28x+182 im used to putting them on the left side0= x^2-15x+182

Answer 48

Are you sure that it is positive 182?

Answer 49

oh see told ya lol

Answer 50

So could you please write the correct equation for me? Thank you.

Answer 51

15\[15+-\sqrt{953}\div2\]

Answer 52

omg just one little negative threw my whole answer off ugh

Answer 53

No, that is not what I asked.

Answer 54

well i got my answer with your wonderful help

Answer 55

Yes, you did get the answer but you didn't answer my question. lol. Please do not skip steps on the test. Never be brave and skip steps unless you know your stuff well.

Answer 56

Good work! GOOD LUCK on all your exams!

Answer 57

i didnt skip I had done that part really easy

Answer 58

Thank you again for you help probably will need your help again soon. lol

Answer 59

I have to log out now, but I will probably be back in a few hours if you need me. Take care and please try to get some sleep. lol

Answer 60

ok thank you and you to.