5/(2x)  4/(x^{2}) = 7/(2x^{2})
First, set the equation equal to 0 by moving all the terms to one side of the equation. For simplicity, subtract 7/(2x^{2}) from both sides of the equation:
5/(2x)  4/(x^{2})  7/(2x^{2}) = 0
Now we went to generate a least common denominator among all terms on the left hand side of the equation. Notice that 2x^{2} is the least common denominator here, so we want to manipulate all of the terms in a way such that they all have a denominator of 2x^{2}. To do this, multiply the numerator and the denominator of the first term by x and multiply the numerator and the denominator of the second term by 2:
5(x)/(2x)(x)  4(2)/(x^{2})(2)  7/(2x^{2}) = 0
5x/(2x^{2})  8/(2x^{2})  7/(2x^{2}) = 0
Since all the terms now share a common denominator, we can add their numerators:
(5x  8  7)/(2x^{2}) = 0
(5x  15)/(2x^{2}) = 0
After we crossmultiply, we arrive at the following:
5x  15 = 0
Adding 15 to both sides of the equation we get the following:
5x = 15
Divide both sides of the equation by 5 to solve for x:
x = 3
2/1/2013

Tamara J.