Question

Simplify
(5xr)/(3x^(2)y)+(7xr)/(3y)

Answer 1

The simplified expression is
`(5r+7x^2r)/3xy`. This result is obtained by finding a common denominator, combining fractions, and factoring out common terms, yielding a simplified form.

Let's evaluate the simplification:

`\[ (5xr)/(3x^2y) + (7xr)/(3y) \]`

To combine the fractions, find a common denominator, which is
`\(3x^2y\)`:

`\[ (5xr \cdot 3y)/(3x^2y \cdot 3y) + (7xr \cdot 3x^2y)/(3y \cdot 3x^2y) \]`

Simplify the numerators:

`\[ (15xyr)/(9x^2y) + (21x^2yr)/(9x^2y) \]`

Combine the numerators:

`\[ (15xyr + 21x^2yr)/(9x^2y) \]`

Factor out common terms:

`\[ (3xr(5y + 7x))/(9x^2y) \]`

Now, simplify the fraction by canceling common factors:

`\[ (5r+7x^2r)/(3xy) \]`

The simplified expression is
`\((5r+7x^2r)/(3xy)\)`.