Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Let's start with the given equation:
[tex]\[ c = \frac{a}{a + b} \][/tex]
We need to isolate \( a \) in terms of \( b \) and \( c \).
Step 1: Multiply both sides by \( (a + b) \) to clear the fraction:
[tex]\[ c(a + b) = a \][/tex]
Step 2: Distribute \( c \) on the left-hand side:
[tex]\[ ca + cb = a \][/tex]
Step 3: Move all terms involving \( a \) to one side of the equation. Subtract \( a \) from both sides:
[tex]\[ ca - a = -cb \][/tex]
Step 4: Factor \( a \) out on the left-hand side:
[tex]\[ a(c - 1) = -cb \][/tex]
Step 5: Divide both sides by \( (c - 1) \) to isolate \( a \):
[tex]\[ a = \frac{-cb}{c - 1} \][/tex]
To simplify the expression, we can multiply the numerator and the denominator by \(-1\):
[tex]\[ a = \frac{cb}{1 - c} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{a = \frac{bc}{1 - c}} \][/tex]
The correct choice is:
(A) [tex]\(a = \frac{bc}{1 - c}\)[/tex]
[tex]\[ c = \frac{a}{a + b} \][/tex]
We need to isolate \( a \) in terms of \( b \) and \( c \).
Step 1: Multiply both sides by \( (a + b) \) to clear the fraction:
[tex]\[ c(a + b) = a \][/tex]
Step 2: Distribute \( c \) on the left-hand side:
[tex]\[ ca + cb = a \][/tex]
Step 3: Move all terms involving \( a \) to one side of the equation. Subtract \( a \) from both sides:
[tex]\[ ca - a = -cb \][/tex]
Step 4: Factor \( a \) out on the left-hand side:
[tex]\[ a(c - 1) = -cb \][/tex]
Step 5: Divide both sides by \( (c - 1) \) to isolate \( a \):
[tex]\[ a = \frac{-cb}{c - 1} \][/tex]
To simplify the expression, we can multiply the numerator and the denominator by \(-1\):
[tex]\[ a = \frac{cb}{1 - c} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{a = \frac{bc}{1 - c}} \][/tex]
The correct choice is:
(A) [tex]\(a = \frac{bc}{1 - c}\)[/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.