[tex] \frac{1}{6x {(x - 2)}^{2} } - \frac{1}{4 {x}^{2}(x - 2) } \\ = \frac{4x}{4x} \times \frac{1}{6x {(x - 2)}^{2} } - \frac{6(x - 2)}{6(x - 2)} \times \frac{1}{4 {x}^{2}(x - 2) } \\ = \frac{4x}{24 {x}^{2} {(x - 2)}^{2} } - \frac{6(x - 2)}{24 {x}^{2} {(x - 2)}^{2}} \\ = \frac{4x - 6(x - 2)}{24 {x}^{2} {(x - 2)}^{2} } \\ = \frac{4x - 6x + 12}{24 {x}^{2} {(x - 2)}^{2} } \\ = \frac{12 - 2x}{24 {x}^{2} {(x - 2)}^{2} }\\= \frac{12 - 2x}{24{x}^{2}({x}^{2}-4x+4)}\\=\frac{12-2x}{24{x}^{4}-96{x}^{3}+96{x}^{2}}\\=\frac{6-x}{12{x}^{4}-48{x}^{3}+48{x}^{2}}[/tex]
You multiply by fractions which have the same numerator and denominator, which equal one so you do not change the expression, to make the denominators of the fractions the same. Then you can subtract the numerator from the other, expand, and simplify.
