$\frac{ 5\left( x+3 \right)+x \times \left( x+1 \right) }{ \left( x+1 \right) \times \left( x+3 \right) }$
Distribute $5$ through the parentheses$\frac{ 5x+15+x \times \left( x+1 \right) }{ \left( x+1 \right) \times \left( x+3 \right) }$
Distribute $x$ through the parentheses$\frac{ 5x+15+{x}^{2}+x }{ \left( x+1 \right) \times \left( x+3 \right) }$
Simplify the expression$\frac{ 5x+15+{x}^{2}+x }{ {x}^{2}+3x+x+3 }$
Collect like terms$\frac{ 6x+15+{x}^{2} }{ {x}^{2}+3x+x+3 }$
Collect like terms$\frac{ 6x+15+{x}^{2} }{ {x}^{2}+4x+3 }$
Use the commutative property to reorder the terms$\frac{ {x}^{2}+6x+15 }{ {x}^{2}+4x+3 }$