Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To solve the equation
[tex]\[ \frac{x^2 + 5}{x + 5} = \frac{3}{x + 5} \][/tex]
we follow these steps:
1. Identify Common Denominator:
Since both sides of the equation have the same denominator [tex]\(x + 5\)[/tex], we can equate the numerators directly (provided [tex]\(x \neq -5\)[/tex] to avoid division by zero).
2. Equate the Numerators:
Set the numerators equal to each other:
[tex]\[ x^2 + 5 = 3 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
Rearrange the equation to solve for [tex]\(x\)[/tex]:
[tex]\[ x^2 + 5 = 3 \][/tex]
Subtract 5 from both sides:
[tex]\[ x^2 = 3 - 5 \][/tex]
Simplify the right-hand side:
[tex]\[ x^2 = -2 \][/tex]
4. Consider the Result:
Taking the square root of both sides, we get:
[tex]\[ x = \sqrt{-2} \][/tex]
The square root of a negative number is not a real number. Therefore, [tex]\(x = \sqrt{-2}\)[/tex] does not produce any real solutions.
Since the problem requires real solutions, we conclude that:
[tex]\[ \boxed{\text{There are no real solutions.}} \][/tex]
[tex]\[ \frac{x^2 + 5}{x + 5} = \frac{3}{x + 5} \][/tex]
we follow these steps:
1. Identify Common Denominator:
Since both sides of the equation have the same denominator [tex]\(x + 5\)[/tex], we can equate the numerators directly (provided [tex]\(x \neq -5\)[/tex] to avoid division by zero).
2. Equate the Numerators:
Set the numerators equal to each other:
[tex]\[ x^2 + 5 = 3 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
Rearrange the equation to solve for [tex]\(x\)[/tex]:
[tex]\[ x^2 + 5 = 3 \][/tex]
Subtract 5 from both sides:
[tex]\[ x^2 = 3 - 5 \][/tex]
Simplify the right-hand side:
[tex]\[ x^2 = -2 \][/tex]
4. Consider the Result:
Taking the square root of both sides, we get:
[tex]\[ x = \sqrt{-2} \][/tex]
The square root of a negative number is not a real number. Therefore, [tex]\(x = \sqrt{-2}\)[/tex] does not produce any real solutions.
Since the problem requires real solutions, we conclude that:
[tex]\[ \boxed{\text{There are no real solutions.}} \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.