Simplify the product $\frac{5}{n+1} \cdot \frac{n+1}{n+3}$
Answer (2)
Multiply the fractions: n + 1 5 ⋅ n + 3 n + 1 = ( n + 1 ) ( n + 3 ) 5 ( n + 1 ) .
Cancel the common factor ( n + 1 ) from the numerator and denominator.
The simplified expression is n + 3 5 .
Explanation
Understanding the Expression We are given the expression n + 1 5 ⋅ n + 3 n + 1 and we want to simplify it.
Multiplying the Fractions To simplify the expression, we multiply the two fractions: n + 1 5 ⋅ n + 3 n + 1 = ( n + 1 ) ( n + 3 ) 5 ( n + 1 )
Canceling the Common Factor Now, we can cancel the common factor of ( n + 1 ) from the numerator and the denominator, assuming n = − 1 : ( n + 1 ) ( n + 3 ) 5 ( n + 1 ) = n + 3 5
Final Simplified Expression Therefore, the simplified expression is n + 3 5 .
Examples
Imagine you're baking a cake and need to adjust the recipe based on the number of guests. If the original recipe calls for n + 1 5 cups of flour and you're scaling it by a factor of n + 3 n + 1 , simplifying the expression helps you quickly determine the adjusted amount of flour needed. This type of simplification is useful in various real-life scenarios where you need to scale quantities or adjust proportions based on changing factors.
The product n + 1 5 ⋅ n + 3 n + 1 simplifies to n + 3 5 after canceling the common factor n + 1 from the numerator and denominator. This cancellation is valid if n is not equal to -1. Always check for such conditions when simplifying fractions.
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