For anyone who is really good at math?

Question

Solve the equation for all the solutions of x:

35/(x-2) + 35/(x+2) = 6

Answer 1

We need to use the quadratic identity (x+2) (x-2) = x^2 - 2^2

Multiply the equation on both sides by (x+2) (x-2).

What we will get is
35(x+2) + 35(x-2) = 6 (x+2) (x-2)
35x + 70 + 35x - 70 = 6x^2 - 24
70x = 6x^2 -24

Rearranging so that one side of the equation is zero,
6x^2 - 70x -24 = 0

Divide both sides by 2,
3x^2 - 35x -12 = 0

Factorise into
(3x+1) (x-12) = 0

Thus 3x+1 =0
or x-12 = 0

The answers are x= -1/3 or x=12

I hope this helps.

Answer 2

35 / (x-2) + 35 / (x+2 ) = 6
1/(x-2) + 1/(x+2) = 6/35

x has two values one with addition and one with subtraction,

addition:
so simple way is to split 6/35 into two numbers
35 = 5 * 7 (the difference is only 2 but we need difference of 4)
so mutiply by 4
6/35 = 24/140 = (1/14 + 1/10)

hence x is 12

subtraction:
35 = 5*7 so subtracting 1/5 - 1/7 = 2/35 but numerator is 6 so,
6/35 = 3/5 - 3/7

so x is -1/3

so solutions of x is 12 an -1/3

Answer 3

[35(x+2) + 35(x-2)]/ (x-2)(x+2) = 6
35[x+2 + x- 2]/ [x^2+ 2x -2x -4] = 6
35[2x] = 6[x^2 -4]
70x = 6x^2 - 24
0=6x^2 -70x - 24
0=3x^2 - 35x - 12
0 =x^2 - 35/3x - 4
=>
1st value :
--------------
x(3x-35) = 12

x = 12

12(36 -35) = 12

2nd value = -1/3

-1/3 (-1/3*3 - 35) = 12

Answer 4

multiply both sides by (x-2)(x+2)

35(x+2)+35(x-2)=6x^2 -24

Coolecting like terms and dividing by 2

3x^2-35x-12 = 0

Factorising

(3x+1)(x-12)=0

====> x=-1/3 or x=12

Answer 5

x = 12 or x = -1/3

Answer 6

multiply both sides by (x-2)(x+2)
this gives:
35(x+2) + 35(x-2) =6(x+2)(x-2)

70x = 6x^2 -24

6x^2 - 70x -24 =0

solve the quadratic equation

Answer 7

(35(x+2) + 35(x-2))/((x-2)(x+2)) = 6

x does not = 2 nor -2

35x + 70 + 35x - 70 = 6
70x = 6
x = 3/35

Answer 8

step#1:
multiply both sides by (x-2)(x+2);
we get;
35(x+2)+35(x-2)=6(x+2)(x-2)

step#2:
35x+70+35x-70=6x^2-12x+12x-24
after solving we get the equation as
6x^2-70x-24=0

step#3:
divide both by 2;

3x^2-35x-12=0;

do the mid-term break;

3x^2-36x+x-12=0;
3x(x-12)+1(x-12)=0;
(x-12)(3x+1)=0;
either
(x-12)=0------(i)
or
(3x+1)=0------(ii)

after solving (i) and (ii) we get
x=12 and x=-1/3

Answer 9

35/(x-2)+35/(x+2)=6
[35/1(1/x-2)]+[35/1(1/x+2)]=6
35x-70+35x+70=6
70x=6
x=6/70
x=3/35
x=11.66 or 12

Answer 10

he he he nakakatawa ang mg aalgebra nyo ito ang tamang solution;

35/(x-2) + 35/(x+2) = 6

Cross multiply :

35(x+2) + 35(x-2)
------------------------ = 6
(x-2) (x+2)

35x + 70 + 35X - 70
-------------------------- = 6
(x² - 4)

70x
----------- = 6
(x²-4)

70x = 6(x²- 4)

70x = 6x² - 24 or

6x² - 70x - 24 = 0

Solving using the quadratic equation formula
-B ± (B² - 4AC)^1/2 ----meaning square root of B² - 4AC
x = ----------------------------------
2A
70 ± (70² - 4(24)(6))^1/2
x = -------------------------------------
2(24)

x = 70 ± 65.75
----------------
48

x = 0.088 ; x = 2.83 ans.