Math Problem Statement
Solution
The question provided asks to find the value of that makes the two vectors and equal.
To solve this, we need to set the two expressions equal and solve for :
Step-by-step solution:
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Cross-multiply to get rid of the fractions:
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Expand the right-hand side:
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Rearrange the equation to set it equal to 0:
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Factor the quadratic equation:
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Set each factor equal to zero:
Thus, the possible values for are and .
However, looking at the options, only fits (as is not listed). Therefore, the correct answer is Option d: and .
Would you like further details or have any other questions?
Related Questions:
- How would the solution change if the expression for was ?
- What happens if you replace the vector with ?
- How can you solve a quadratic equation like using the quadratic formula?
- What if the equation was , how would you solve that?
- Can this method be generalized for other rational expressions?
Tip:
When solving equations with fractions, cross-multiplying is a quick way to eliminate the denominators and simplify the process!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Rational Equations
Formulas
a = t / (t + 1)
b = t / 2
Setting the two expressions equal and solving for t: (t / (t + 1)) = (t / 2)
Theorems
Cross-multiplication to eliminate fractions
Suitable Grade Level
Grade 9-10