can someone show me these steps with the division like
2
---
1 which would mean half. the following though. so i can see it.
Simplify
3
--- + 1
x-5
-----------
1 - (4)/(x-5)
Get least common denominator.
For top part, the LCD is x-5. So the 1 becomes (x-5)/(x-5). Thus the top becomes (3 + x - 5)/(x - 5). This simplifies to (x-2)/(x-5).
Now do the bottom. The LCD is x-5. So the 1 becomes (x-5)/(x-5). So, the whole bottom part becomes (x-5-4)/(x-5).
This simplifies to (x-9)/(x-5).
Now you have complex fraction, where the top is: (x-2)/(x-5); and the bottom is (x-9)/(x-5). The (x-5)'s cancel, so you're left with:
(x-2)/(x-9).
I got the same answer. Hope I didn't make a mistake.
The top part, however, is not 1/2. It is 2.
Matt
Just to make sure, I added a random # in for x (7)
Both answers came to -2.5
Matt
To simplify the given expression step by step, we have:
1. Start with the expression:
3
--- + 1
x-5
-----------
1 - (4)/(x-5)
2. Find the least common denominator (LCD) for the top and bottom parts separately.
- For the top part: The LCD is (x-5). The 1 becomes (x-5)/(x-5). Thus, the top part becomes (3 + x - 5)/(x - 5), which simplifies to (x-2)/(x-5).
- For the bottom part: The LCD is also (x-5). The 1 becomes (x-5)/(x-5). So, the bottom part becomes (x-5-4)/(x-5), which simplifies to (x-9)/(x-5).
3. Now you have a complex fraction, where the numerator is (x-2)/(x-5) and the denominator is (x-9)/(x-5).
4. To simplify this complex fraction, multiply the numerator by the reciprocal of the denominator.
- Multiply the numerator (x-2)/(x-5) by (x-5)/(x-9).
This gives ((x-2)(x-5))/((x-5)(x-9)), which further simplifies to (x-2)/(x-9).
5. Now, you have the simplified form: (x-2)/(x-9).
It is important to note that the numerical value of the expression depends on the value of x. In the example you provided with x=7, both answers came out to be -2.5. However, the value of the simplified expression will vary for different values of x.