Someone please help me with this 10th grade math problem.?

Question

x+4/x + 3/x-4 = -16/x^2 -4x

This has been driving me crazy.

I keep getting it down to 'no solution' but i don't think that's the answer.

Can someone confirm it for me or explain how to do the problem correctly. Please and Thank you.

Answer 1

Check out this website.

www.webmath.com

They will walk you through it all.

I get x= -1 when I do it by hand.  

technically it could be laid out as...

1/10 (9 +/- (thats plus or minus) i sqrt(239)

Answer 2

This does not look right but heres what I did. Also there are no parenthesis so I kind of guessed what was under what.

x+4/x + 3/x-4 = -16/x^2 -4x

5x+(7/x)-4=(16/x^2) -then times both sides by X^2

5x^3+7x=20

x(5x^2+7-20)

X=0 and 5X^2-13=0

              x^2=13/5

               X=square root of 13/5

Answer 3

LCD =x^2 -4x =x(x-4)l When you multiply through, you get:

x^2(x-4) +4(x-4) +3x =-16

x^3 -4x^2 +4x -16 +3x +16=0

x^3 -4x^2 -x =0

x(x^2 -4x -1) =0

x=0 can't be a solution, it puts a zero in the denominator

x^2 -4x +4 = 1 +4

(x-2)^2 =5

x-2 = +/- sqrt 5

x =2 +sqrt 5 or 2- sqrt 5

If you mean (x+4) / 4 then you get x^2 +3x=0 and x=-3 is the only solution.

Answer 4

I get the same thing as I can't find a reference for the symbol between x and 2

Answer 5

Please clarify the order of operations (PEMDAS)?

is left side four terms (interpreted as written)?

x

+ 4/x

+ 3/x

- 4

or three terms? :

x

+ 4/x

+ 3/(x-4)

?

Similarly, right side: 2 terms (interpreted as written)?

-16/x^2

-4x

or 1 term?

-16/(x^2-4x)

This is Algebra I review, yes?

Edit:

Consider left equation:

Multiply (x+4) / x by (x-4)/(x-4) and 3 / (x-4) by x/x

this gives:

((x+4)(x-4) + 3x) / (x(x-4)) = -16 / (x(x-4))

cancel out the common denominator (x(x-4)) leaving:

(x+4)(x-4) + 3x = -16

distribute:

x^2 + 3x -16 = -16

x^2 +3x = 0

factor:

x(x+3) = 0

solutions are:

x = 0

x = -3