Problem:
4x/(x+2)-8/(x-1)
What I Got:
4x^2-4x-16/(x+2)(x+1)
*I had to simplify the rational expression
No. At x=0, it doesn't check. The starting problem gives 8, your answer gives -8. I suspect a sign error somewhere. Probably in the denominator, the x+1 should be x-1
To simplify the rational expression (4x/(x+2))-8/(x-1), we need to find a common denominator and combine the fractions.
Here are the steps to simplify the expression:
1. Find a common denominator:
The denominators are (x+2) and (x-1). The common denominator is (x+2)(x-1).
2. Expand the expression:
Multiply each term by the appropriate factor to obtain a common denominator.
For the first fraction, multiply both the numerator and denominator by (x-1):
(4x(x-1))/((x+2)(x-1)) = (4x^2-4x)/((x+2)(x-1))
For the second fraction, multiply both the numerator and denominator by (x+2):
(-8(x+2))/((x-1)(x+2)) = (-8x-16)/((x-1)(x+2))
3. Combine the numerators:
Now, we can combine the two fractions by adding their numerators over the common denominator.
(4x^2-4x-8x-16)/((x+2)(x-1))
= (4x^2-12x-16)/((x+2)(x-1))
Finally, the simplified expression is (4x^2-12x-16)/((x+2)(x-1)).
Please note that in the original expression, there was an error in the denominator where it should be (x-1) instead of (x+1). This correction is reflected in the simplified expression above.