Question

Factorise
x^3-1÷x^3-2x+2÷x

Answer 1

${x}^{3} - 1 \div {x}^{3} - 2x + 2 \div x \\ = ({x}^{3} - 1 \div {x}^{3}) - 2(x - 1 \div x) \\ = (x - 1 \div x)( {x}^{2} + x \times 1 \div x + 1 \div {x}^{2} ) - 2(x - 1 \div x) \\ = (x - 1 \div x)( {x}^{2} + 1 + 1 \div {x}^{2} - 2) \\ = (x - 1 \div x)( {x}^{2} - 1 + 1 \div {x}^{2} )$