(9a^3b^4-12a^2b^5+6ab^7)/(6a^2b^3)
( 9 a ^ 3 b ^ 4 - 12 a ^ 2 b ^ 5 + 6 a b ^ 7) / ( 6 a ^ 2 b ^3 ) =
3 * a * b ^ 3 * ( 3 a ^ 2 * b - 4 a * b ^ 2 + 2 b ^ 4 ) / [ 3 * a * b ^ 3 * ( 2 a ) ] =
( 3 a ^ 2 b - 4 a b ^ 2 + 2 b ^ 4 ) / 20
Sorry last row :
= ( 3 a ^ 2 b - 4 a b ^ 2 + 2 b ^ 4 ) / 2 a
To simplify the expression (9a^3b^4 - 12a^2b^5 + 6ab^7) / (6a^2b^3), you can follow these steps:
Step 1: Simplify the coefficients.
The numerator has coefficients of 9, -12, and 6, while the denominator has a coefficient of 6. We can simplify the coefficients by dividing each term by 6:
(9 / 6)a^3b^4 - (12 / 6)a^2b^5 + (6 / 6)ab^7.
Simplifying further, we have:
(3/2)a^3b^4 - 2a^2b^5 + ab^7.
Step 2: Simplify the variables.
Next, let's simplify the variables in each term:
(a^3/a^2)b^4 - (a^2/a^2)b^5 + (a/a^2)b^7.
Simplifying the exponents, we have:
a^(3-2)b^4 - a^(2-2)b^5 + a^(1-2)b^7.
This gives:
ab^4 - b^5 + (1/a)b^7.
Finally, we can rewrite the expression as:
ab^4 - b^5 + b^7/a.
So, the simplified expression is ab^4 - b^5 + b^7/a.