Final answer:
To simplify (7)/(x-6)+5 to one fraction, you must obtain a common denominator, combine the terms, and simplify. The resulting fully simplified expression is (5x-23)/(x-6).
Step-by-step explanation:
To fully simplify the expression (7)/(x-6)+5 into one fraction, you must find a common denominator. The common denominator, in this case, is (x-6), because the first term already has this and the second term is a whole number which can be thought of as being over 1. To combine these terms, you apply the following steps:
- Multiply 5 by (x-6) to give it the same denominator. This changes the equation to (7)/(x-6) + (5(x-6))/(x-6).
- Distribute the 5 inside the parentheses: (7)/(x-6) + (5x-30)/(x-6).
- Combine the numerators over the single common denominator: (7+5x-30)/(x-6).
- Simplify the numerator by combining like terms: (5x-23)/(x-6).
- Check if the numerator and denominator can be factored further and reduced, but in this case, they cannot.
Therefore, the fully simplified form of (7)/(x-6)+5 is (5x-23)/(x-6).