(4m-9n-9n^2÷16m^2)+1÷4m-3n
8m - 12n - 9n^2 + 16m^2 + 1,
16m^2 + 8m - 9n^2 - 12n + 1,
8m(2m + 1) - 3n(3n + 4) + 1,
as written, using PEMDAS, this parses out as
(4m-9n-9n^2÷16m^2)+1÷4m-3n
= 4m - 9n - (9n^2/16m^2) + 1/(4m) - 3n
Maybe you meant
((4m-3n-9n^2)÷16m^2 + 1)÷(4m-3n)
= (4m-3n-9n^2+16m^2)÷(16m^2(4m-3n))
= (4m-3n+(4m-3n)(4m+3n)) ÷ (16m^2(4m-3n))
= (4m-3n)(4m+3n+1) ÷ (16m^2(4m-3n))
= (4m+3n+1) ÷ 16m^2
That's not quite what you had, but maybe if you used some of your own parentheses, things would be clearer
To simplify the given expression (4m-9n-9n^2÷16m^2)+1÷4m-3n, let's break it down step by step.
Step 1: Simplify the numerator of the fraction 9n^2 ÷ 16m^2:
To divide terms with exponents, we subtract the exponents. In this case, we have n^2 ÷ m^2, so we subtract the exponents as follows: 9n^(2-2) = 9n^0 = 9.
So, 9n^2 ÷ 16m^2 simplifies to 9 ÷ 16m^2.
Step 2: Simplify the expression inside the parentheses:
The expression inside the parentheses can be simplified by grouping like terms. We have 4m and -9n, where both terms have different variables (m and n) with different exponents and coefficients.
Therefore, (4m - 9n - 9n^2 ÷ 16m^2) simplifies to (4m - 9n - (9 ÷ 16m^2)).
Step 3: Simplify the expression outside the parentheses:
Now, we have the expression (4m - 9n - (9 ÷ 16m^2)) + 1 ÷ 4m - 3n. We'll work on simplifying this step by step.
First, let's simplify the fraction 1 divided by 4m:
To divide 1 by 4m, we multiply by the reciprocal of 4m, which is 1 ÷ 4m = 1 × 1 ÷ 4m = 1 ÷ 4m.
Then, we have (4m - 9n - (9 ÷ 16m^2)) + 1 ÷ 4m - 3n = (4m - 9n - (9 ÷ 16m^2)) + 1 ÷ 4m - 3n.
Finally, we can rearrange the terms in a more organized way:
(4m - 9n) - (9 ÷ 16m^2) + (1 ÷ 4m) - 3n.
And there you have it! The simplified expression is (4m - 9n) - (9 ÷ 16m^2) + (1 ÷ 4m) - 3n.