1 + 1/μ + γ/μ ÷ 1/100 + 1/λ0 + γ/16.
Understand the Problem
The question is asking to solve a mathematical expression that involves fractions and variables. The goal is to simplify or compute the value of the expression given in the image.
Answer
$$1 + \frac{1 + 100\gamma}{\mu} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
Answer for screen readers
The final simplified expression is: $$1 + \frac{1 + 100\gamma}{\mu} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
Steps to Solve
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Rearrange the Expression Start with the given expression: $$1 + \frac{1}{\mu} + \frac{\gamma}{\mu} \div \frac{1}{100} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
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Handle the Division Evaluate the division by $\frac{1}{100}$: $$\frac{\gamma}{\mu} \div \frac{1}{100} = \frac{\gamma}{\mu} \times 100 = \frac{100\gamma}{\mu}$$
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Rewrite the Expression Now substitute back into the expression: $$1 + \frac{1}{\mu} + \frac{100\gamma}{\mu} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
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Combine Similar Terms Combine the terms that involve $\frac{1}{\mu}$: $$1 + \left(\frac{1 + 100\gamma}{\mu}\right) + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
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Final Expression This gives you the final simplified expression: $$1 + \frac{1 + 100\gamma}{\mu} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
The final simplified expression is: $$1 + \frac{1 + 100\gamma}{\mu} + \frac{1}{\lambda_0} + \frac{\gamma}{16}$$
More Information
This expression combines constant terms and various variables, showing how they interact through fractions and coefficients. Understanding the simplification helps in performing further operations in complex equations or physics problems involving these variables.
Tips
- Forgetting to multiply by the reciprocal when dividing by a fraction.
- Not properly combining like terms.
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