If this is your equation: [tex] \frac{2}{5} + \frac{3}{5x} = \frac{x+5}{10} [/tex]
Solution:
LCD for 5 and 5x is 5x
[tex] \frac{x}{x} ( \frac{2}{5} )+ \frac{3}{5x} = \frac{x+5}{10} [/tex]
[tex] \frac{2x}{5x} + \frac{3}{5x} = \frac{x+5}{10} [/tex]
[tex] \frac{2x+3}{5x} = \frac{x+5}{10} [/tex]
[tex]10(2x+3)=5x(x+5)[/tex] ←cross product
20x + 30 = 5x² + 25x ←simplify with distributive property
0 = 5x² + 5x - 30 ←use inverse operations to collect all terms on one side
0 = x² + x - 6 ←if possible divide by numerical GCF (This case 5)
0 = (x + 3)(x - 2) ←Factor
x = -3 or x = 2
Please check by substitution in original equation... Both work
