Solve for: (p^2-36)/(3p-4) * (3p^2+11p-20)/(p^2+11p+30)

Expression: $\frac{ {p}^{2}-36 }{ 3p-4 } \times \frac{ 3{p}^{2}+11p-20 }{ {p}^{2}+11p+30 }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3{p}^{2}+11p-20 }{ {p}^{2}+11p+30 }$

Write $11p$ as a difference

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3{p}^{2}+15p-4p-20 }{ {p}^{2}+11p+30 }$

Write $11p$ as a sum

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3{p}^{2}+15p-4p-20 }{ {p}^{2}+6p+5p+30 }$

Factor out $3p$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3p \times \left( p+5 \right)-4p-20 }{ {p}^{2}+6p+5p+30 }$

Factor out $-4$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3p \times \left( p+5 \right)-4\left( p+5 \right) }{ {p}^{2}+6p+5p+30 }$

Factor out $p$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3p \times \left( p+5 \right)-4\left( p+5 \right) }{ p \times \left( p+6 \right)+5p+30 }$

Factor out $5$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ 3p \times \left( p+5 \right)-4\left( p+5 \right) }{ p \times \left( p+6 \right)+5\left( p+6 \right) }$

Factor out $p+5$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ \left( p+5 \right) \times \left( 3p-4 \right) }{ p \times \left( p+6 \right)+5\left( p+6 \right) }$

Factor out $p+6$ from the expression

$\frac{ \left( p-6 \right) \times \left( p+6 \right) }{ 3p-4 } \times \frac{ \left( p+5 \right) \times \left( 3p-4 \right) }{ \left( p+6 \right) \times \left( p+5 \right) }$

Cancel out the common factor $p+6$

$\frac{ p-6 }{ 3p-4 } \times \frac{ \left( p+5 \right) \times \left( 3p-4 \right) }{ p+5 }$

Cancel out the common factor $p+5$

$\frac{ p-6 }{ 3p-4 } \times \left( 3p-4 \right)$

Cancel out the common factor $3p-4$

$p-6$