Simplify (5a^2-5(a^2+2ah+h^2))/ha^2(a+h)^2
To simplify the given expression, we can start by factoring out common terms.
Step 1: Let's start by factoring out -5 from the numerator:
-5(a^2 + 2ah + h^2)
Step 2: Now, let's factor the numerator further:
-5((a + h)^2)
Step 3: Next, let's factor out common terms from the denominator:
ha^2(a + h)^2
Now we can simplify the expression by canceling out common factors. In this case, we can divide -5(a + h)^2 by ha^2(a + h)^2:
-5(a + h)^2 / ha^2(a + h)^2
The (a + h)^2 terms in the numerator and denominator can be canceled out, leaving us with:
-5 / ha^2
So, the simplified expression is -5 / ha^2.
Let's simplify step by step:
First, let's distribute the -5 to each term inside the parentheses:
-5 * a^2 = -5a^2
-5 * 2ah = -10ah
-5 * h^2 = -5h^2
So now our expression becomes: (5a^2 - 5a^2 - 10ah - 5h^2) / ha^2(a+h)^2
The two terms with a^2 cancel each other out, leaving us with:
(-10ah - 5h^2) / ha^2(a+h)^2
Next, let's simplify the denominator:
a^2(a+h)^2 = a^2(a^2+2ah+h^2) = a^4 + 2a^3h + a^2h^2
Now our expression becomes: (-10ah - 5h^2) / (ha^4 + 2ha^3h + ha^2h^2)
Combining like terms inside the numerator:
-10ah - 5h^2 = -5h(2a + h)
Now our expression becomes: (-5h(2a + h)) / (ha^4 + 2ha^3h + ha^2h^2)
Finally, our completely simplified expression is: (-5h(2a + h)) / (ha^4 + 2ha^3h + ha^2h^2)
To simplify the expression, let's break it down step by step:
Step 1: Distribute the -5 to the terms inside the parentheses:
(5a^2 - 5a^2 - 10ah - 5h^2) / ha^2(a + h)^2
Simplifies to:
(-10ah - 5h^2) / ha^2(a + h)^2
Step 2: Factor out a -5 from the numerator:
(-5(2ah + h^2)) / ha^2(a + h)^2
Step 3: Cancel out the common factor h in the numerator and denominator:
(-5h(2a + h)) / ha^2(a + h)^2
Step 4: Cancel out the common factor a in the numerator and denominator:
(-5h(2 + h)) / h(a + h)^2
Step 5: Finally, cancel out the common factor h in the numerator and denominator:
(-5(2 + h)) / (a + h)^2
Therefore, the simplified expression is:
(-5(2 + h)) / (a + h)^2