\frac{10\left(\left(622\right)\left(377\right)\right)-\left(622\right)\left(377\right)}{\left[10\left(622^{2}\right)-\left(622\right)^{2}\right]-\left[10\left(377^{2}\right)-\left(377\right)^{2}\right]}

asked by guest
on Dec 08, 2024 at 4:34 am



You asked:

Evaluate the expression: \(\frac{10 \cdot 622 \cdot 377 - 622 \cdot 377}{10 \cdot {622}^{2} - {622}^{2} - \left(10 \cdot {377}^{2} - {377}^{2}\right)}\)

MathBot Answer:

\[\frac{10 \cdot 622 \cdot 377 - 622 \cdot 377}{10 \cdot {622}^{2} - {622}^{2} - \left(10 \cdot {377}^{2} - {377}^{2}\right)} = \frac{234494}{244755} = 0.9\overline{580764437907295050152193009335866478723621}\]


\[\begin{aligned}\frac{10 \cdot 622 \cdot 377 - 622 \cdot 377}{10 \cdot {622}^{2} - {622}^{2} - \left(10 \cdot {377}^{2} - {377}^{2}\right)}& = \left(10 \cdot 622 \cdot 377 - 622 \cdot 377\right) \cdot \frac{1}{10 \cdot 622^{2} - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = \left(6220 \cdot 377 - 622 \cdot 377\right) \cdot \frac{1}{10 \cdot 622^{2} - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = \left(2344940 - 622 \cdot 377\right) \cdot \frac{1}{10 \cdot 622^{2} - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = \left(2344940 - 234494\right) \cdot \frac{1}{10 \cdot 622^{2} - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{10 \cdot 622^{2} - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{10 \cdot 386884 - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 622^{2} - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 386884 - \left(10 \cdot 377^{2} - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 386884 - \left(10 \cdot 142129 - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 386884 - \left(1421290 - 377^{2}\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 386884 - \left(1421290 - 142129\right)}\\& = 2110446 \cdot \frac{1}{3868840 - 386884 - 1279161}\\& = 2110446 \cdot \frac{1}{3481956 - 1279161}\\& = \frac{2110446}{2202795}\\& = \frac{234494}{244755}\end{aligned}\]