Add the rational expressions:
6

x+7
+
8

x+7
.

Simplify if possible.

Question

Add the rational expressions: 
6

x+7
+
8

x+7
.

Simplify if possible.

BlackTom AI · Accepted Answer

The problem asks to Add the rational expressions: 6/(x+7) + 8/(x+7) and simplify if possible.
First, observe that both fractions share the same denominator (x+7). When adding fractions with the same denominator, you add the numerators while keeping the common denominator: 6 + 8 becomes 14, so the sum is 14/(x+7).
Next, check if the resulting fraction can be simplified further. Since 14 is a constant numeric numerator and (x+7) is a linear polynomial in the denominator, there is no common polynomial factor to cancel (unless x were restricted to a specific value that makes numerator share a factor with the denominator, which is not the case here for a generic variable x). Therefore, no further algebraic simplification is possible.
Finally, consider the domain: the expression is defined for all x except where the denominator is zero, so x ≠ -7. This ensures the original expressions are valid and the result is valid as well.
In summary, adding the two fractions with the same denominator yields 14/(x+7), and there is no further simplification beyond this, with the understanding that x ≠ -7.

ALGII141-027 5.4 Practice Problems

Add the rational expressions: 6 x+7 + 8 x+7 . Simplify if possible.

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