Adding Rational Expressions 9x/(6-x) + 6x/(x-6) Simplified

Published on November 2, 2026

Algebra

Add the rational expressions 9x/(6-x) and 6x/(x-6) by rewriting 6-x as -(x-6) to get a common denominator, then combine numerators and reduce to lowest terms, giving 3x/(6-x).

Question

What is the answer to this

Answer

Step 1: Rewrite the denominators with a common form.

Since

Step 2: Add the fractions over the common denominator .

Step 3: Reduce.

The numerator

and denominator

share no common factor, so the expression is in lowest terms. Writing the denominator as

gives an equivalent form:

Final answer:

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