Rational Expressions
Writing equivalent rational expressions with polynomial denominators
Fill in the blank to make equivalent rational expressions.
\[
\frac{3}{v+2}=\frac{\square}{(v+5)(v+2)}
\]
Answer
Final Answer: The equivalent rational expression is \(\frac{3v + 15}{(v+5)(v+2)}\). So, the blank should be filled with \(\boxed{3v + 15}\).
Step 1 ：The given expression is \(\frac{3}{v+2}\) and we need to find the equivalent expression with the denominator \((v+5)(v+2)\).
Step 2 ：To find the equivalent expression, we can multiply the numerator and denominator of the given expression by \((v+5)\).
Step 3 ：This gives us the equivalent expression as \(3*(v + 5)\), which simplifies to \(3v + 15\).
Step 4 ：This is the numerator of the equivalent rational expression with the denominator \((v+5)(v+2)\).
Step 5 ：Final Answer: The equivalent rational expression is \(\frac{3v + 15}{(v+5)(v+2)}\). So, the blank should be filled with \(\boxed{3v + 15}\).
