How do I subtract this rational problem?
2x-1/x+4 - x+4/1
I was thinking multiplying x+4 with x+4 but then I would get x^2+8x+16.
Then do that,and you can factor the quadratic to (x+4)^2
what's the answer if I subtract 2x-1 from (x+4)^2
To subtract rational expressions like the one you provided, you need to find a common denominator for the fractions. Let's break down the steps:
1. Factor the denominators:
The denominator of the first fraction is (x+4), and the denominator of the second fraction is 1 (which can be written as 1/1).
2. Find a common denominator:
In this case, the common denominator will be (x+4), since it is a factor of both denominators.
3. Adjust the numerators:
To adjust the numerators, multiply the first fraction's numerator (2x - 1) by (1/1) and multiply the second fraction's numerator (x + 4) by (x + 4).
4. Simplify the expression:
Now that you have a common denominator, you can subtract the fractions.
(2x - 1)/1 * (x + 4)/(x + 4) = (2x^2 + 8x - x - 4)/(x + 4)
Simplifying further, (2x^2 + 7x - 4)/(x + 4)
So, the simplified form of the rational expression is (2x^2 + 7x - 4)/(x + 4).