Question

Solve the equation below.


`(x+4)/(6x) =(1)/(x)`

A. x= -2
B. x=0,2
C. x= 2
D. x=0,-2

Answer 1

Option C is correct.

Explanation:

We need to solve the equation below and find value of x

`(x+4)/(6x) =(1)/(x)`

Cross multiply

x(x+4)=6x

x^2+4x=6x

x^2+4x-6x=0

x^2-2x=0

Taking x common

x(x-2)=0

x=0 and x-2 =0

x=0 and x= 2

Verify solutions

putting x=0

x+4/6(0) = 1/0

the solution is undefined.

Putting x = -2

2+4/6(2) = 1/2

2+4/12 = 1/2

6/12=1/2

1/2=1/2

the solution is defined.

The solutions is x=2 as for x=0 the solution is undefined.

So, Option C is correct.

Answer 2

B. x=0,2

Explanation:

(x+4) 1

-------- = -----

6x x

Using cross products

x * (x+4) = 1*6x

Distribute

x^2 +4x = 6x

Subtract 6x from each side

x^2 +4x-6x = 6x-6x

x^2 -2x = 0

Factor out an x

x (x-2) = 0

Using the zero product property

x=0 x-2 =0

x=0 x-2+2 =0+2

x =0 x=2