Question

if a-1/a=8 and a≠0 find a+1/a and a²-1/a²​

Answer 1

Answer:

$\frac{a - 1}{a} = 8 \\ a - 1 = 8a \\ - 1 = 8a - a \\ - 1 = 7a \\ \boxed{\underline{ \underline{ \bf\frac{ - 1}{7}}} = a} \\ \\ \frac{a + 1}{a} \\ = ( \frac{ - 1}{7} + 1) \div \frac{ - 1}{7} \\ = ( \frac{ - 1 + 7}{7} ) \div \frac{ - 1}{7} \\ = \frac{6}{7} \div \frac{ - 1}{7} \\ = \frac{6}{ \cancel7} \times \frac{ \cancel7}{ - 1} \\ \boxed{ = \underline{ \underline{ \bf - 6}}} \\ \\ \frac{ {a}^{2} - 1 }{ {a}^{2} } \\ = ({ (\frac{ - 1}{7}) }^{2} - 1) \div { (\frac{ - 1}{7}) }^{2} \\ = (\frac{1}{49} - 1) \div (\frac{1}{49} ) \\ = (\frac{1 - 49}{49} ) \div (\frac{1}{49} ) \\ = \frac{ - 48}{49} \div \frac{1}{49} \\ = \frac{ - 48}{ \cancel{49}} \times \frac{ \cancel{49}}{1} \\ \boxed{ = \underline{ \underline{ \bf- 48}}}$