(x^5/x^2 6x 9) (5/x^2 5x 6)
To simplify the expression (x^5/x^2 + 6x + 9)(5/x^2 + 5x + 6), we can use the distributive property to multiply each term in the first expression by each term in the second expression.
Let's break it down step by step:
Step 1: Multiply the first terms in each expression:
(x^5/x^2) * (5/x^2) = (x^5 * 5) / (x^2 * x^2) = (5x^5) / (x^4)
Step 2: Multiply the first terms in each expression:
(x^5/x^2) * (5x) = (x^5 * 5x) / (x^2) = (5x^6) / (x^2) = 5x^4
Step 3: Multiply the first terms in each expression:
(x^5/x^2) * (6) = (x^5 * 6) / (x^2) = 6x^5 / x^2 = 6x^3
Step 4: Multiply the second terms in each expression:
(6x) * (5/x^2) = (6x * 5) / (x^2) = (30x) / (x^2) = 30/x
Step 5: Multiply the second terms in each expression:
(6x) * (5x) = 30x^2
Step 6: Multiply the second terms in each expression:
(6x) * (6) = 36x
Step 7: Multiply the third terms in each expression:
(9) * (5/x^2) = (9 * 5) / (x^2) = (45) / (x^2)
Step 8: Multiply the third terms in each expression:
(9) * (5x) = 45x
Step 9: Multiply the third terms in each expression:
(9) * (6) = 54
Now, let's combine all the terms we obtained:
(5x^5) / (x^4) + 5x^4 + 6x^3 + 30/x + 30x^2 + 36x + 45/x^2 + 45x + 54
This is the simplified expression.