equation. show your solution?

Question

2/x + 5/(x-1) = 6

(4n+2)/3 + 1 = 2/n

Answer 1

solving...

2/x + 5/(x-1) = 6

Multiply terms by 1 to get common demoninators

2/x * (x-1)/(x-1) + 5/(x-1) * x/x = 6 * x*(x-1)/ (x*(x-1))

2*(x-1)/(x*(x-1)) + 5x/(x*(x-1) = 6 * x*(x-1)/ (x*(x-1))

Now multiply equation by x*(x-1) to get rid of denominators

2*(x-1) + 5x = 6x*(x-1)

Use distribution to get rid of parens ()

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

Now add like terms and move everything to the right...

0 = 6x^2 - 13x + 2

Now it's just a simple quadratic equation.. Solve as usual..

(6x-1)(x-2) = 0

x = 1/6 or 2

---------------------------

(4n + 2) / 3 + 1 = 2/n

Multiply terms by 1 to get common demoninators..

(4n+2)/3 * n/n + 1* 3n/3n = 2/n * 3/3

n*(4n+2) / 3n + 3n/3n = 6/3n

Multiply by 3n to get rid of denominators

n*(4n+2) + 3n = 6

Distribute to get rid of parens ()

4n^2 + 2n + 3n = 6

Move all terms to one side and add like terms...

4n^2 + 5n - 6 = 0

Now it's just a simple quadratic equation.. Solve as usual..

(4n-3)(n+2) = 0

n = 3/4 or -2

Answer 2

Q1: 2/x + 5/(x-1) = 6

Then,
[2(x-1) +5(x)]/ x(x-1) = 6

(2x - 2 + 5x)/ (x^2 - x) = 6

Thus,
6x^2 - 6x = 2x - 2 + 5x
6x^2 - 6x - 2x -5x + 2 = 0
6x^2 -13x +2 = 0

Therefore:
6x -1 = 0 and x = -2
x = 1/6


Q2: (4n+2)/3 + 1 = 2/n

Then,
make the denominator the same:
(4n+2+3)/3 = 2/n

Cross multiply:
4n^2 + 2n + 3n = 6

Bring them all to one side:
4n^2 + 2n + 3n -6 = 0

Then:
4n - 3 =0 and n= 2
4n = 3
n = 3/4

Answer 3

2/x + 5(x-1) = 6
2x-2 + 5x = 6x^2-6x
6x^2-13x +2 = 0
(6x-1)(x-2)=0
x=1/6 and x=2

4n^2 + 2n + 3n = 6
4n^2 + 5n - 6 = 0
(4n-3)(n+2) = 0
n=3/4 and n=-2

Answer 4

I have one. We don't like our variable in the denominator. Period.

So, you have to get x and x-1 out of the denominator. It's like when you add 2/3 and 4/7. Find the LCD. Here, it's x(x-1).

Multiply both sides by x(x-1).

(x(x-1))2 + 5(x(x-1)) = 6 (x(x-1))
---------- -----------
x x - 1

2(x - 1) + 5x = 6(x^2 - x)

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

7x -2 = 6x^2 - 6x
+6x + 6x
-------------------------------------------------------
13x - 2 = 6x^2
-13x -13x
------------------------------------------------------
-2 = 6x^2 - 13x
+2 +2
------------------------------------------------------------
0 = 6x^2 - 13x + 2 Now factor.
0 = (6x -1) (x - 2)

0 = 6x - 1 or 0 = x - 2

x = 1/6 or x = 2

Answer 5

1.LCD=x(x-1)
2x-2+5x=6x(x-10)
7x-2=6x^2-6x
6x^2-13x+2=0
6x(x-2)-1(x-2)=0
(x-2)(6x-1)=0
so x=2 or 1/6

2.4n+2+3=6/n
4n^2+5n=6
4n^2+5n-6=0
=>4n^2+8n-3n-6=0

(4n-3)(n+2)=0
n=3/4 or -2