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\(\frac{{{a^2}b}}{{a{b^2}}} = \frac{{a \times a \times b}}{{a \times b \times b}}\)

\(\frac{{{a^2}b}}{{a{b^2}}} = \frac{{a \times a \times b}}{{a \times b \times b}} = \frac{{1 \times a \times 1}}{{1 \times 1 \times b}} = \frac{a}{b}\)

Notice the common factor of \(2t - 1\) on the numerator and denominator, so expand the fraction to see where to 'cancel'.

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

\(= \frac{{(2t - 1)(2t - 1)}}{1} = {(2t - 1)^2}\)

\(\frac{{{x^2} + 4x}}{{{x^2} - 16}} = \frac{{x(x + 4)}}{{(x - 4)(x + 4)}}\)

Now we can divide top and bottom by \(x + 4\)

\(\frac{{{x^2} + 4x}}{{{x^2} - 16}} = \frac{{x(x + 4)}}{{(x - 4)(x + 4)}} = \frac{x}{{x - 4}}\)