x/(x-3)-4-(2x-5)/(x+2)
If the problem is this:
x/(x - 3) - 4 - (3x - 5)/(x + 2)
...find a common denominator to start.
The common denominator is (x - 3)(x + 2), then convert each term using the common denominator.
Here's a start:
[x(x + 2)/(x - 3)(x + 2)] - [4(x - 3)(x + 2)]/(x - 3)(x + 2) - [(2x - 5)(x - 3)]/(x - 3)(x + 2) =
I'll let you take it from here. Remember to use the distributive property to distribute the negative!
I hope this will help and is what you were asking.
One correction!
I meant to type this for the problem:
x/(x - 3) - 4 - (2x - 5)/(x + 2)
The rest is OK. Sorry for any confusion!
but when I do this I get
x^2+2x-4x^2+4x+24-2x^2+x+15
solving this I get
(-5x^2+7x+39)/(x-3)(x+2)
The answer in the book however says
-(5x^2-17x-9)/(x-3)(x+2)
so I don't know what I am doing wrong, can you take me step by step through the problem. I have a lot of problems, but I think once I understand what I am doing wrong with this one I can get the rest.
The top should be this:
x^2 + 2x - 4x^2 + 4x + 24 - 2x^2 + 11x - 15
Combining like terms:
-5x^2 + 17x + 9
Factoring out the negative gives this:
-(5x^2 - 17x - 9)
This should help you see the answer given:
-(5x^2-17x-9)/(x-3)(x+2)
I hope this helps. Watch those negative signs because they can be tricky on these types of problems!
To solve the expression x/(x-3)-4-(2x-5)/(x+2), we need to find a common denominator to combine the terms.
The common denominator is (x-3)(x+2), so we need to convert each term to have this denominator.
First, let's work on the first term x/(x-3). To convert it, we multiply the numerator and denominator by (x+2):
(x * (x+2))/((x-3) * (x+2)) = (x^2 + 2x)/((x-3)(x+2))
Next, let's work on the second term -4. To convert it, we multiply it by ((x-3)(x+2))/((x-3)(x+2)):
-4 * ((x-3)(x+2))/((x-3)(x+2)) = -4(x-3)(x+2)/((x-3)(x+2))
Now, let's work on the third term (2x-5)/(x+2). To convert it, we multiply the numerator and denominator by (x-3):
((2x - 5) * (x - 3))/((x+2) * (x-3)) = (2x^2 - 11x + 15)/((x+2)(x-3))
Now that all the terms have the same denominator, let's combine them:
(x^2 + 2x)/((x-3)(x+2)) - 4(x-3)(x+2)/((x-3)(x+2)) - (2x^2 - 11x + 15)/((x+2)(x-3))
Expanding the terms, we get:
(x^2 + 2x - 4x^2 + 12x - 8 - 2x^2 + 11x - 15)/((x-3)(x+2))
Combining like terms, we get:
(-5x^2 + 25x - 23)/((x-3)(x+2))
Factoring out the negative, we get:
-(5x^2 - 25x + 23)/((x-3)(x+2))
So, the correct answer is -(5x^2 - 25x + 23)/((x-3)(x+2))
I apologize for any confusion caused by the previous incorrect response.
To solve the expression x/(x - 3) - 4 - (2x - 5)/(x + 2), let's go through the steps:
Step 1: Find a common denominator: To add or subtract fractions, we need a common denominator. In this case, the common denominator is (x - 3)(x + 2), since it includes both denominators.
Step 2: Convert each term using the common denominator:
- For the first term, x/(x - 3), the denominator is already the common denominator.
- For the second term, 4, we multiply it by (x - 3)(x + 2)/(x - 3)(x + 2) to give: 4(x - 3)(x + 2)/(x - 3)(x + 2).
- For the third term, (2x - 5)/(x + 2), the denominator is already the common denominator.
So, the expression becomes:
x/(x - 3) - 4(x - 3)(x + 2)/(x - 3)(x + 2) - (2x - 5)/(x + 2)
Step 3: Simplify and combine like terms:
- For the first term, x/(x - 3), we leave it as is.
- For the second term, we can distribute the 4 and simplify: -4(x - 3)(x + 2)/(x - 3)(x + 2) = -4.
- For the third term, (2x - 5)/(x + 2), we leave it as is.
So, the expression simplifies to:
x/(x - 3) - 4 - (2x - 5)/(x + 2)
Step 4: Combine the terms:
The expression becomes:
x/(x - 3) - 4 - (2x - 5)/(x + 2)
Step 5: Simplify further if possible:
To simplify, let's find a common denominator for the first two terms:
- For the first term, x/(x - 3), the denominator is (x - 3).
- For the second term, -4, we can rewrite it as -4(x - 3)/(x - 3) to give: -4(x - 3)/(x - 3).
So, the expression becomes:
[x - 4(x - 3)]/(x - 3) - (2x - 5)/(x + 2)
Simplifying further, we have:
[x - 4x + 12)/(x - 3) - (2x - 5)/(x + 2)
Combine like terms in the numerator:
(-3x + 12)/(x - 3) - (2x - 5)/(x + 2)
To subtract the fractions, we need a common denominator, which is (x - 3)(x + 2). We can convert each fraction:
(-3x + 12)(x + 2)/(x - 3)(x + 2) - (2x - 5)(x - 3)/(x - 3)(x + 2)
Now, we can subtract the fractions:
(-3x^2 + 6x + 24 - 2x^2 + 6x + 15)/(x - 3)(x + 2)
Combine like terms in the numerator:
(-5x^2 + 12x + 39)/(x - 3)(x + 2)
The simplified expression is:
-(5x^2 - 12x - 39)/(x - 3)(x + 2)
Therefore, the answer in the book, -(5x^2 - 17x - 9)/(x - 3)(x + 2), is the correct simplified form.