(2/7x^2+7x^2y-4y^3)+(7/6x^2-2/5x^2y^2+5y^3)
To simplify the expression (2/7x^2+7x^2y-4y^3) + (7/6x^2-2/5x^2y^2+5y^3), we need to combine like terms and perform any necessary arithmetic operations.
Step 1: Add the coefficients of the terms that have the same variable and the same exponent.
In the expression, we have the following terms:
(2/7x^2 + 7x^2y - 4y^3) + (7/6x^2 - 2/5x^2y^2 + 5y^3)
For x^2:
We have (2/7x^2) + (7/6x^2)
To add these two terms, we first need to find a common denominator for 7 and 6. The least common multiple of 7 and 6 is 42, so we can rewrite the expression as follows:
(12/42x^2) + (49/42x^2)
Now that the denominators are the same, we can simply add the numerators:
(12/42 + 49/42)x^2
= (61/42)x^2
So, we have (61/42)x^2
For x^2y:
We have (7x^2y) + (-2/5x^2y^2)
These terms do not have a common denominator, so we can't directly add them.
For y^3:
We have (-4y^3) + (5y^3)
These terms have the same variable and exponent, so we can simply combine them:
(-4 + 5)y^3
= y^3
Step 2: Rewrite the simplified terms in the final expression.
Using the results from Step 1, we can rewrite the expression:
(61/42)x^2 + y^3
Therefore, the simplified expression is (61/42)x^2 + y^3.