At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Let's solve the equation [tex]\(\frac{x^2 - (x+1)(x+2)}{5x + 1} = 6\)[/tex] step by step.
Step 1: Simplify the numerator:
[tex]\[ x^2 - (x+1)(x+2) \][/tex]
Expand [tex]\((x+1)(x+2)\)[/tex]:
[tex]\[ (x+1)(x+2) = x^2 + 3x + 2 \][/tex]
So, we have:
[tex]\[ x^2 - (x^2 + 3x + 2) = x^2 - x^2 - 3x - 2 = -3x - 2 \][/tex]
Step 2: Substitute the simplified numerator back into the equation:
[tex]\[ \frac{-3x - 2}{5x + 1} = 6 \][/tex]
Step 3: Clear the fraction by multiplying both sides of the equation by [tex]\(5x + 1\)[/tex]:
[tex]\[ -3x - 2 = 6(5x + 1) \][/tex]
[tex]\[ -3x - 2 = 30x + 6 \][/tex]
Step 4: Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
[tex]\[ -3x - 2 - 30x = 6 \][/tex]
[tex]\[ -3x - 30x - 2 = 6 \][/tex]
[tex]\[ -33x - 2 = 6 \][/tex]
Step 5: Isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -33x - 2 + 2 = 6 + 2 \][/tex]
[tex]\[ -33x = 8 \][/tex]
Step 6: Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{8}{-33} \][/tex]
[tex]\[ x = -\frac{8}{33} \][/tex]
Thus, the solution to the equation [tex]\(\frac{x^2 - (x+1)(x+2)}{5x + 1} = 6\)[/tex] is:
[tex]\[ x = -\frac{8}{33} \][/tex]
Step 1: Simplify the numerator:
[tex]\[ x^2 - (x+1)(x+2) \][/tex]
Expand [tex]\((x+1)(x+2)\)[/tex]:
[tex]\[ (x+1)(x+2) = x^2 + 3x + 2 \][/tex]
So, we have:
[tex]\[ x^2 - (x^2 + 3x + 2) = x^2 - x^2 - 3x - 2 = -3x - 2 \][/tex]
Step 2: Substitute the simplified numerator back into the equation:
[tex]\[ \frac{-3x - 2}{5x + 1} = 6 \][/tex]
Step 3: Clear the fraction by multiplying both sides of the equation by [tex]\(5x + 1\)[/tex]:
[tex]\[ -3x - 2 = 6(5x + 1) \][/tex]
[tex]\[ -3x - 2 = 30x + 6 \][/tex]
Step 4: Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
[tex]\[ -3x - 2 - 30x = 6 \][/tex]
[tex]\[ -3x - 30x - 2 = 6 \][/tex]
[tex]\[ -33x - 2 = 6 \][/tex]
Step 5: Isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -33x - 2 + 2 = 6 + 2 \][/tex]
[tex]\[ -33x = 8 \][/tex]
Step 6: Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{8}{-33} \][/tex]
[tex]\[ x = -\frac{8}{33} \][/tex]
Thus, the solution to the equation [tex]\(\frac{x^2 - (x+1)(x+2)}{5x + 1} = 6\)[/tex] is:
[tex]\[ x = -\frac{8}{33} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.