fractions help...?

Question

(9/x-5)-1=(8/x+5)

that is

9/x-5 -1 = 8/x+5

Answer 1

multiply all numerators, by LCD=(x-5)(x+5)
to get.


x=11, x=-10

Answer 2

A. Eliminate fractions-multiply the denominators by everything:

(x-5)(x+5)[(9/x-5)] - (x-5)(x+5)(1) = (x-5)(x+5)[(8/x+5)]

B. Cancel "like" terms and combine remaining terms >

(x+5)(9) - (x-5)(x+5)(1) = (x-5)(8)
9x + 45 - (x^2 + 5x - 5x - 25) = 8x - 40
9x + 45 - x^2 + 25) = 8x - 40

C. Set the equation to "0" > add 40 to both sides > subtract 8x from both sides >

9x + 45 - x^2 + 25 + 40 = 8x - 40 + 40
9x + 45 - x^2 + 25 + 40 - 8x = 8x - 8x
9x + 45 - x^2 + 25 + 40 - 8x = 0

First: combine "like" terms & rewrite in alpha descending order:

- x^2 + x + 110 = 0

Sec: factor out a -1 from the equation and factor the equation in the parenthesis >

-1(x^2 - x - 110) = 0
-1(x-11)(x+10) = 0

Third: set both parenthesis to equal "0" and solve for "x" >

x - 11 = 0
x - 11 +11 = 0+11
x = 11

x + 10 = 0
x + 10 - 10 = 0 - 10
x = -10

Answer 3

i assume it's: 9/(x - 5) - 1 = 8/(x + 5)

9/(x - 5) - (x - 5)/(x - 5) = 8/(x + 5)
(9 - x + 5)/(x - 5) = 8/(x + 5)
(14 - x)/(x - 5) = 8/(x + 5)

now cross multiply,

(14 - x)(x + 5) = 8(x - 5)
14x + 70 - x^2 - 5x = 8x - 40

move everything to one side,

- x^2 + x + 110 = 0

factor or use quadratic formula,

-(x^2 - x - 110) = 0
x^2 - x - 110 = 0 >>>(0/-1 = 0)
(x + 10)(x - 11) = 0
x = -10, 11

plug the nuumbers back in the equation,

when x = -10,

9/(-10 - 5) - 1 = 8/(-10 + 5)
-3/5 - 1 = -8/5
-8/5 = -8/5

when x = 11,

9/(11 - 5) - 1 = 8/(11 + 5)
3/2 - 1 = 1/2
1/2 = 1/2

therefore, x = -10, 11

Answer 4

9/x -5 -1 = 8/x + 5
Basically for this kind of problem, start by making all the fraction into digit number by multiplying it with the denominator in this case which is x. This will give you

9/x X x - 5 X x - 1 X x = 8/x X x + 5 X x
9-5x-1x = 8+5x (Add up all the x)
9-6x=8+5x (bring -6x to right hand side and 8 to left hand side)
9-8=5x+6x
1=11x (bring 11 over)
1/11=x
x = 0.09 (rounding to 2 decimal place)

To double check your answer, always substitutes the answer into the equation :

9/x -5 -1 = 8/x + 5
9/0.09-5-1 = 8/0.09+5
100-5-1=88.89+5
94=93.89 (slight different due to rounding)

Answer 5

(9/x - 5) - 1 = (8/x + 5)

9 - 5x + x = 8 + 5x

9 - 8 = 6x + 5x

1 = 11x

x = 1/11

Answer 6

first you have to multiply to get rid of the bottoms of these equations

x . [(9/x -5) -1] = x[8/x +5] ~then~9 - 5x - x = 8 +5x~then~9- 6x = 8 +5x~then~9 - 8 = 5x + 6x~then~1 = 11x~then ou get~x= 1/11 as your answer

Answer 7

9/x - 8/x = 5+1+5
1/x = 11
1 = 11x
x = 1/11
S = {x E R | x = 1/11}
..:..

Answer 8

first thing is to multiply to get rid of the bottoms of the equations

x . [(9/x -5) -1] = x[8/x +5]

9 - 5x - x = 8 +5x

9- 6x = 8 +5x

9 - 8 = 5x + 6x

1 = 11x

x = 1/11