How to Algebraically Solve Fractions With Variables
- 1). Solve the rational equation (5 / (x + 2)) + (2 / x) = (3 / 5x). Begin by finding the least common denominator. Since x appears in the other two denominators, disregard it and multiply the other two together to form the LCD: (x + 2) * 5x = 5x(x + 2).
- 2). Convert the fractions to the LCD: (5 / (x + 2)) * (5x / 5x) = (25x / 5x(x + 2)); (2 / x) * ((5(x + 2) / 5(x + 2)) = ((10x + 20) / (5(x + 2)); and (3 / 5x) * ((x + 2) / (x + 2)) = ((3x + 6) / (5x(x + 2)).
- 3). Disregard the denominators, since they are now all equal, and rewrite the numerators in terms of the original equation: (25x) + (10x + 20) = 3x + 6. Combine the like terms on the left side: 35x + 20 = 3x + 6. Subtract 20 from both sides: 35x = 3x + -14. Subtract 3x from both sides: 32x = - 14, and divide both sides by 32: x = -14 / 32 or x = - 7 / 16.
