Question

Help, with solving rational equations! I am no good at it :( Solve for x: 2 over 5 plus 3 over 5 x equals quantity x plus 5 over 10. (2 points)
x = -3

x = 2

x = -3 and x = 2

No Solution

Answer 1

If this is your equation: $\frac{2}{5} + \frac{3}{5x} = \frac{x+5}{10}$
Solution:
LCD for 5 and 5x is 5x
$\frac{x}{x} ( \frac{2}{5} )+ \frac{3}{5x} = \frac{x+5}{10}$
$\frac{2x}{5x} + \frac{3}{5x} = \frac{x+5}{10}$
$\frac{2x+3}{5x} = \frac{x+5}{10}$
$10(2x+3)=5x(x+5)$ ←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