Help! On Solving Rational Equations! Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10. (2 point) x = -4 x = 5 x = -4 and x = 5 No Solution

If this is your equation [tex] \frac{1}{2} + \frac{4}{2x} = \frac{x+4}{10} [/tex], then I would add the two fraction of the left by getting the LCD (lowest or least common denominator after which I would use cross-product. (Whispers you could just plug in the answer choices to see which one works)

Back to work: LCD of 2 and 2x is 2x 
[tex] \frac{x}{x} ( \frac{1}{2} )+ \frac{4}{2x} = \frac{x+4}{10} [/tex]
[tex] \frac{x}{2x} + \frac{4}{2x} = \frac{x+4}{10} [/tex]
[tex] \frac{x+4}{2x} = \frac{x+4}{10} [/tex] ←after adding the fractions did you notice that the numerators are equal therefore the denominators must be equal
2x = 10  
x = 5 when you divide both sides by 2... please check your answer