Bobbie Comstock

2022-01-12

Solve the given problem.

In analyzing the tuning of an electronic circuit, the expression

$[\omega {\omega}_{0}^{-1}-{\omega}_{0}{\omega}^{-1}]}^{2$

is used. Expand and simplify this expression.

In analyzing the tuning of an electronic circuit, the expression

is used. Expand and simplify this expression.

jean2098

Beginner2022-01-13Added 38 answers

Step 1

To simplify the following expression.

$[\omega {\omega}_{0}^{-1}-{\omega}_{0}{\omega}^{-1}]}^{2$

Evaluate$\omega}_{0}^{-1$ and $\omega}^{-1$ using this exponent rule $a}^{n}=\frac{1}{{a}^{n}$ as follows:

$={[\frac{\omega}{{\omega}_{0}}-\frac{{\omega}_{0}}{\omega}]}^{2}$

To subtract these fractions, consider the LCM:$\left(\omega {\omega}_{0}\right)$ as common denominator

Multiply the first fraction by$\omega$ and the second fraction by $\omega$ as follows:

$={[\frac{\omega {\omega}_{0}}{\omega {\omega}_{0}}-\frac{\omega {\omega}_{0}}{\omega {\omega}_{0}}]}^{2}$

Subtract the numerators and put the result on the LCM as follows:

$={\left[\frac{\omega {\omega}_{0}-\omega {\omega}_{0}}{\omega {\omega}_{0}}\right]}^{2}$

$={\left[\frac{0}{\omega {\omega}_{0}}\right]}^{2}$

Apply this exponent rule$\frac{0}{a}=0,\text{}a\ne 0$

$={\left[0\right]}^{2}=0$

Answer: 0

To simplify the following expression.

Evaluate

To subtract these fractions, consider the LCM:

Multiply the first fraction by

Subtract the numerators and put the result on the LCM as follows:

Apply this exponent rule

Answer: 0

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