Question

simplify. (5^-1-4^-1)^-1+(2^-1-3^-1)-1​

Answer 1

Answer:

${\longrightarrow{\boxed{\bold{-14}}}}$

Step-by-step explanation:

$\longrightarrow\rm{\bigg( 5^{-1} - 4^{-1} \bigg)^{-1} + \bigg(2^{-1} - 3^{1} \bigg)^{-1}}$

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$\longrightarrow\rm{\bigg(\dfrac{1}{5} - 4^{-1}\bigg)^{-1} + \bigg(2^{-1} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{\bigg(\dfrac{1}{5} - 4\bigg)^{-1} + \bigg(2^{-1} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{\bigg(\dfrac{-1}{20}\bigg)^{-1} + \bigg(2^{-1} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{\dfrac{20}{-1} + \bigg(2^{-1} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{-20 + \bigg(2^{-1} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{-20 + \bigg(\dfrac{1}{2} - 3^{-1}\bigg)^{-1}}$

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$\longrightarrow\rm{-20 + \bigg(\dfrac{1}{2} - \dfrac{1}{3}\bigg)^{-1}}$

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$\longrightarrow\rm{-20 + \bigg(\dfrac{1}{60}\bigg)^{-1}}$

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$\longrightarrow\rm{-20 + 6}$

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${\longrightarrow{\boxed{\bold{-14}}}}$

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Therefore, -14 is the required simplified form.

Answer 2

Question :

We have been asked to find out the sum of (5-¹ - 4-¹)-¹ and (2-¹ - 3-¹)-¹ .

Answer :

-14

Full solution In the attachment.

Steps followed :

1. Firstly we have both the terms . Then solved each separately.
2. Then to make the powers positive ; we have taken the fractional forms. That is taking the negative powered number in fractional form where the numerator is 1.
3. Then we took the LCM of denominators and simplified the numerators with them.
4. Then again reciprocated the solution we got as the whole powers was -1.
5. Then in first case ; transferred the power of denominator to numerator.
6. Same steps were followed with the second part.
7. Final solutions were added.
8. Obtained final answer as -14.