Final answer:
To solve the equation (1)/(2)+(1)/(2x)=(x²-7x+10)/(4x), rewrite it and cross multiply to eliminate the fractions. Then, solve the resulting quadratic equation by factoring or using the quadratic formula.
Step-by-step explanation:
To solve the equation (1)/(2)+(1)/(2x)=(x²-7x+10)/(4x), we need to rewrite it in a different form. First, we can find the common denominator for the left side of the equation, which is 2x. So, the equation becomes (x+1)/(2x) + 1/(2x) = (x²-7x+10)/(4x). Then, we can combine the fractions on the left side by adding the numerators over the common denominator: (x+1+1)/(2x) = (x²-7x+10)/(4x).
Next, we can cross multiply to get rid of the fractions. Multiply the left numerator (x+2) by the right denominator (4x) and the right numerator (x²-7x+10) by the left denominator (2x). This gives us (x+2)*4x = (x²-7x+10)*2x.
After expanding and simplifying both sides of the equation, we can solve for x. The resulting quadratic equation is 2x²-15x+20 = 0, which can be factored as (2x-5)(x-4) = 0. Therefore, the two possible values for x are x = 5/2 or x = 4.