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How Do You Add Two Rational Expressions with the Same Denominator?

Simplify the equation on the right into one rational expression.

Summary

  1. Since we have a common denominator, we can just add the numerators straight across
  2. Drop the parentheses by distributing the signs inside
  3. The numerator looks like 2x+5+8x-10
  4. Now add together the like terms:
  5. 2x plus 8x equals 10x
  6. 5 minus 10 equals -5

Notes

    1. The two rational expressions are being added together
    1. The denominator is the bottom of the fraction, and in this case, it is x-7
    1. The common denominator is x-7
    2. The numerators are 2x+5 and 8x-10
    1. The new numerator is over the common denominator
    1. (2x+5) becomes just 2x+5, and (8x+10) becomes 8x+10
    1. (2x+5)+(8x+10) becomes 2x+5+8x+10
    1. 2x and 8x are like terms
    1. 5 and -10 are like terms