x^2-4/x^2+3x+2
4x^2-y^2/y-2x
I need help with these problem
factor the numerators:
1) factors to (x+2)(x-2), and the denominator factors to (x+2)(x+1)
2. numerator factors to (2x-y)(2x+y) which is equal to -1(y-2x)(y+2x)
To simplify these expressions, we'll start by factoring the denominators. Let's solve them step by step:
1) Simplifying (x^2-4)/(x^2+3x+2)
To simplify this expression, we need to factor the numerator and denominator.
The numerator, x^2 - 4, can be written as (x+2)(x-2) using the difference of squares formula.
The denominator, x^2 + 3x + 2, can be factored as (x+1)(x+2) using the product-sum method.
Now we can rewrite the expression as [(x+2)(x-2)]/[(x+1)(x+2)].
Next, we cancel out the common factor of (x+2) in the numerator and denominator to simplify further:
[(x+2)(x-2)]/[(x+1)(x+2)] = (x-2)/(x+1)
So, the simplified expression is (x-2)/(x+1).
2) Simplifying (4x^2-y^2)/(y-2x)
To simplify this expression, we also need to factor the numerator and denominator.
The numerator, 4x^2 - y^2, is a difference of squares and can be factored as (2x + y)(2x - y).
The denominator, y - 2x, cannot be factored further.
Now we can rewrite the expression as [(2x + y)(2x - y)]/(y - 2x).
No further simplification is possible since there are no common factors we can cancel out in this case.
So, the expression (4x^2-y^2)/(y-2x) remains as it is.
Remember, factoring is an essential skill when simplifying algebraic expressions. If you encounter any expressions that are not easily factorable, you can try other techniques such as completing the square or using the quadratic formula.