Question 343339
(1)/(4)+(1)/(6)=(1)/(x)

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(1)/(x)=(1)/(4)+(1)/(6)

To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is 12.  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(1)/(x)=(1)/(6)*(2)/(2)+(1)/(4)*(3)/(3)

Complete the multiplication to produce a denominator of 12 in each expression.
(1)/(x)=(2)/(12)+(3)/(12)

Combine the numerators of all fractions that have common denominators.
(1)/(x)=(2+3)/(12)

Add 3 to 2 to get 5.
(1)/(x)=(5)/(12)

Since there is one rational expression on each side of the equation, this can be solved as a ratio.  For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
1*12=5*x

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
5*x=1*12

Multiply 5 by x to get 5x.
5x=1*12

Multiply 1 by 12 to get 12.
5x=12

Divide each term in the equation by 5.
(5x)/(5)=(12)/(5)

Simplify the left-hand side of the equation by canceling the common factors.
x=(12)/(5)
answer 12/5 or your could break it down more and say
(12)/(5)

The approximate value of (12)/((5)) is 2.4.
2.4