How Do You Add Fractions With Variables?

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When adding and subtracting fractions, you have to rewrite the fractions so they have like denominators. If the fractions have variables, the terms are not always easy to combine, but the process is the same. No calculator is needed.

  1. Find the lowest common denominator

    The lowest (or least) common denominator (LCD) of two fractions is the lowest common multiple (LCM) of both denominators. For example, if the expression adds 1/3 to 1/2, the LCD is 6, because 6 is the lowest number perfectly divisible by both 2 and 3. For the expression 2/x + 3x/2, 2x is the LCD. Until the value of the variable is known, the lowest term perfectly divisible by both 2 and x is 2x.

  2. Change the numerator to fit the new denominator

    A fraction's value is not affected when its numerator and denominator are multiplied by the same number. For example, 1/3 = 1/3 * 2/2 = 2/6. Multiply both the numerator and the denominator by the number that produces the new denominator. This process is sometimes called cross multiplying. 2/x + 3x/2 = (2/x * 2/2) + (3x/2 * x/x) = 4/2x + (3x^2)/2x

  3. Add the terms

    Add the numerators together. Put their sum above a single common denominator. 4/2x + (3x^2)/2x = (3x^2 + 4)/2x Simplify if possible.