Please help me solve these two equations!!
Divide and express as a polynomial:
12a^8b^5 - 9a^14b^15 + 6a^6b^10
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3a^2b^5
Simplify:
a/b - b/a
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a-b/b
check your typing, is this the way you wanted it to look like ?
Don't try to form fractions
instead place numerator and denominatr within brackets and use / to show the division bar.
e.g. (4x -9)/(x^2+6x-7)
4a^6 - 3a^12 b^10 + 2a^4 b^5
(a/b-b/a) / (a-b)/b
= (a^2-b^2)/ab * b/(a-b)
= (a+b)(a-b)/ab * b/(a-b)
= (a+b)/a
To divide and express the given expression as a polynomial, we need to divide each term of the numerator by the denominator.
Step 1: Divide the coefficients:
In this case, 12 divided by 3 is 4.
Step 2: Divide the variables with exponents:
The variable 'a' is raised to different powers in each term. To divide 'a' terms, subtract the exponents.
The first term is 'a^8' divided by 'a^2', which gives us 'a^(8-2) = a^6'.
The second term is 'a^14' divided by 'a^2', which gives us 'a^(14-2) = a^12'.
The third term is 'a^6' divided by 'a^2', which gives us 'a^(6-2) = a^4'.
Similarly, for 'b' terms, we subtract the exponents.
The first term is 'b^5' divided by 'b^5', which gives us 'b^(5-5) = b^0 = 1'.
The second term is 'b^15' divided by 'b^5', which gives us 'b^(15-5) = b^10'.
The third term is 'b^10' divided by 'b^5', which gives us 'b^(10-5) = b^5'.
After dividing each term, we get the expression:
4a^6b^0 - 3a^12b^10 + 2a^4b^5
Now, let's simplify the second expression:
To simplify the given expression, a/b - b/a, we first need to find a common denominator.
The common denominator for a/b and b/a is (a * a) = a^2 and (b * b) = b^2.
Multiplying the numerator and denominator of the first fraction by a, we get:
(a * a) / (b * a)
Multiplying the numerator and denominator of the second fraction by b, we get:
(b * b) / (a * b)
Now, the expression becomes: (a^2) / (ba^2) - (b^2) / (ab^2)
Next, find the least common multiple of the two denominators, which is (ab^2).
Multiplying the first fraction by (a * b), we get:
(a^3 * b) / (a^2b^3)
Multiplying the second fraction by (a * b), we get:
(ab^3) / (a^2b^3)
Now, the expression becomes: (a^3 * b) / (a^2b^3) - (ab^3) / (a^2b^3)
To combine the fractions, we need to have the same denominator. Since the denominators are already the same, we can subtract the numerators:
(a^3 * b - ab^3) / (a^2b^3)
Therefore, the simplified expression is: (a^3 * b - ab^3) / (a^2b^3)
I hope this helps! Let me know if you have any further questions.