Calculate: (5)/(x+1)+(x)/(x+3)

Expression: $\frac{ 5 }{ x+1 }+\frac{ x }{ x+3 }$

Write all numerators above the least common denominator $\left( x+1 \right) \times \left( x+3 \right)$

$\frac{ 5\left( x+3 \right)+x \times \left( x+1 \right) }{ \left( x+1 \right) \times \left( x+3 \right) }$

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

$\frac{ {x}^{2}+6x+15 }{ {x}^{2}+4x+3 }$