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Factorise the numerator \(x^2 + 5x + 4\).

The numbers are +4 and +1 as \(4 \times 1 = 4\) and \(4 + 1 = 5\).

\(x^2 + 5x + 4 = (x + 4)(x + 1)\)

Factorise the denominator \(4x + 16\).

The highest common factor of \(4x\) and 16 is 4. Put this number in front of a bracket and then divide each term by 4 to complete the sum.

\(4x \div 4 = x\) and \(16 \div 4 = 4\).

This gives \(4(x + 4)\).

The original expression was \(\frac{x^2 + 5x + 4}{4x + 16}\). Factorising gives \(\frac{(x + 4)(x + 1)}{4(x + 4)}\).

There is a common factor throughout the fraction of \((x + 4)\). Cancelling out this factor will simplify the expression.

\(\frac{\cancel{(x + 4)}(x + 1)}{4 \cancel{(x + 4)}} = \frac{x + 1}{4}\)