$\frac{ 2\left( x+5 \right) }{ 2{x}^{2}-50 }$
Factor out $2$ from the expression$\frac{ 2\left( x+5 \right) }{ 2\left( {x}^{2}-25 \right) }$
Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression$\frac{ 2\left( x+5 \right) }{ 2\left( x-5 \right) \times \left( x+5 \right) }$
Cancel out the common factor $2$$\frac{ x+5 }{ \left( x-5 \right) \times \left( x+5 \right) }$
Cancel out the common factor $x+5$$\frac{ 1 }{ x-5 }$