Let's simplify the given mathematical expression step-by-step:
Given expression:
[tex]\[ \frac{-7xy}{3x} + \frac{4y^2}{2y} \][/tex]
Step 1: Simplify each term separately.
For the term [tex]\(\frac{-7xy}{3x}\)[/tex]:
- Notice that [tex]\(x\)[/tex] in the numerator and the denominator will cancel each other out.
Thus, we get:
[tex]\[ \frac{-7xy}{3x} = \frac{-7y}{3} \][/tex]
For the term [tex]\(\frac{4y^2}{2y}\)[/tex]:
- Simplify by canceling out [tex]\(y\)[/tex] in the numerator and the denominator.
This results in:
[tex]\[ \frac{4y^2}{2y} = \frac{4y}{2} = 2y \][/tex]
Step 2: Combine the simplified terms.
Now that we have [tex]\(\frac{-7y}{3} + 2y\)[/tex], we need to combine these terms. To do this, we should get a common denominator:
[tex]\[ 2y = \frac{2y \cdot 3}{3} = \frac{6y}{3} \][/tex]
So, the expression becomes:
[tex]\[ \frac{-7y}{3} + \frac{6y}{3} = \frac{-7y + 6y}{3} = \frac{- y}{3} \][/tex]
Therefore, the simplified expression is:
[tex]\[ \frac{-y}{3} \][/tex]
