[tex]\frac{12}{x+7}-\frac{5}{x+7}[/tex]
Answer (1)
Combine the fractions: Since the fractions have a common denominator, combine the numerators: x × 7 12 − 5 .
Simplify the numerator: Perform the subtraction: x × 7 7 .
Cancel the common factor: Divide both the numerator and the denominator by 7: x 1 .
State the final answer: The simplified expression is x 1 .
Explanation
Understanding the Problem We are given the expression x × 7 12 − x × 7 5 . This expression involves the subtraction of two fractions that share a common denominator. Our goal is to simplify this expression into its most basic form.
Combining the Fractions Since both fractions have the same denominator, x × 7 , we can combine them by subtracting the numerators: x × 7 12 − x × 7 5 = x × 7 12 − 5 .
Simplifying the Numerator Now, we simplify the numerator by performing the subtraction: 12 − 5 = 7 .So, the expression becomes: x × 7 7 .
Canceling Common Factors We can rewrite the denominator as 7 x , so the expression is now 7 x 7 . We notice that there is a common factor of 7 in both the numerator and the denominator. We can cancel this common factor to simplify the fraction further: 7 x 7 = ( 7 x ) ÷ 7 7 ÷ 7 = x 1 .
Final Answer Therefore, the simplified expression is x 1 .
Examples
In real-world scenarios, simplifying algebraic expressions like this can be useful in various fields. For example, if you are calculating the flow rate of a fluid through a pipe and the expression for the flow rate involves fractions, simplifying the expression can make the calculations easier and more efficient. Similarly, in electrical engineering, simplifying expressions involving resistance and current can help in circuit analysis.
