Question 159837
X=unknown integer

1/X+1/2X+2=2/3


The common denominator for all is 3(X)(2X+2)

Multiply each term by the common denominator

3(2X+2)+3(X)=2(X)(2X+2)

use the distributive property

6X+6+3X=4x^2+4X
9X+6=4X^2+4X

subtract 9X from each side

6=4X^2-5X

Subtract 6 from both sides
0=4X^2-5X-6

This is a quadratic equation 

Use the quadratic formula to solve*[invoke solve_quadratic_equation 4, -5, -6]

X=2

Plug in 2 for the variable x in the original equatio

1/2+(1/4+2)=2/3
1/2+1/6+2/3

the common denominator is 6

3/6+1/6=4/6 simplify the term to 2/3 by dividing both numerator and denominator by 2