(x)/(x-3)-4-(2x-5)/(x+2)
I posted something before this, so now this is how far I got.
The answer I know is -(5x^2-17x-9)/(x-3)(x+2)
first I get
(x)(x+2)/(x-3)(x+2)- (4)(x-3)(x+2)/(x-3)(x+2)-(2x-5)(x-3)/(x-3)(x+2)
Then I get
x^2+2x-4x^2-4x-24-2x^2-11x+15 (for the top)
When I put everything together I get
(-5x^2 -13x -9)/ (x-3)(x+2)
as you can see however I am having a problem with + and - because I get -13x instead of -17x so could you look at what I am doing wrong and explain it to me?
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!
You made a mistake when combining like terms in the numerator of your expression. Let's go through the steps to get the correct answer.
Starting with the expression:
(x)/(x-3)-4-(2x-5)/(x+2)
First, we need to simplify each term separately. Let's work on the numerators:
For the first term, x/(x-3), we can leave it as is.
For the second term, -4, we can rewrite it as (-4)(1), because (1) is equivalent to (x-3)/(x-3).
For the third term, (2x-5)/(x+2), we can also leave it as is.
Now, let's simplify the terms with the common denominator (x-3)(x+2):
x/(x-3) - 4(1) - (2x-5)/(x+2)
Now, we can combine the terms:
x/(x-3) - 4 - (2x-5)/(x+2)
Next, let's simplify each term:
For the first term, x/(x-3), we can leave it as is.
For the second term, -4, we can rewrite it as (-4)(x-3)/(x-3).
For the third term, (2x-5)/(x+2), we can also leave it as is.
Putting it all together:
x/(x-3) - 4(x-3)/(x-3) - (2x-5)/(x+2)
Now, let's combine the terms in the numerator:
x - 4(x-3) - (2x-5)
Expanding the brackets:
x - 4x + 12 - 2x + 5
Combining like terms:
-x + 17
Finally, factoring out the negative gives us:
-(x - 17)
So, the correct simplified expression is -(x - 17)/(x-3)(x+2).
I apologize for any confusion caused by my previous incorrect explanation.