Evaluate: (2x^2+7x-15)/(x+5)

Expression: $\left( 2{x}^{2}+7x-15 \right)\div\left( x+5 \right)$

Write the division as a fraction

$\frac{ 2{x}^{2}+7x-15 }{ x+5 }$

Write $7x$ as a difference

$\frac{ 2{x}^{2}+10x-3x-15 }{ x+5 }$

Factor out $2x$ from the expression

$\frac{ 2x \times \left( x+5 \right)-3x-15 }{ x+5 }$

Factor out $-3$ from the expression

$\frac{ 2x \times \left( x+5 \right)-3\left( x+5 \right) }{ x+5 }$

Factor out $x+5$ from the expression

$\frac{ \left( x+5 \right) \times \left( 2x-3 \right) }{ x+5 }$

Cancel out the common factor $x+5$

$2x-3$