Question

19 add the rational expressions and simplify the result, if possible. \\(\frac{3z}{y + z} + \frac{3y}{y + z}\\) \\(\frac{3z}{y + z} + \frac{3y}{y + z} = \\) \\(\boxed{}\\) (simplify your answer)

Explanation:

Step1: Add numerators (common denominator)

Since the denominators are the same ($y + z$), we add the numerators: $3z + 3y$.
So the expression becomes $\frac{3z + 3y}{y + z}$.

Step2: Factor numerator

Factor out 3 from the numerator: $3(z + y)$.
Now we have $\frac{3(z + y)}{y + z}$.

Step3: Simplify (cancel common terms)

Notice that $z + y = y + z$, so we can cancel the $y + z$ terms (assuming $y + z
eq 0$).
This gives $\frac{3\cancel{(y + z)}}{\cancel{y + z}} = 3$.

Answer:

3