859/VB02. problem / Math - Solved Math Problems

MR-859 / 3c. problem

Simplify the following expression:

${(\frac{5}{2} - {(\frac{3}{5})}^{- 1})}^{- 1}$

Source: Vene T. Bogoslavov: Collection of Solved Problems #2 - 3.c.)

Algebra → Exponents → Powers

${(\frac{5}{2} - {(\frac{3}{5})}^{- 1})}^{- 1}$

$= {(\frac{5}{2} - {(\frac{5}{3})}^{1})}^{- 1}$

$= {(\frac{5}{2} - \frac{5}{3})}^{- 1}$

$= {(\frac{15}{6} - \frac{10}{6})}^{- 1}$

$= {(\frac{5}{6})}^{- 1}$

$= {(\frac{6}{5})}^{1}$

$= \frac{6}{5}$

$= 1 \frac{1}{5}$

$= 1, 2$