$\left( \frac{ 3 }{ x \times \left( 1-x \right) }+\frac{ 1 }{ 1-x } \right)\div\frac{ 9-{x}^{2} }{ 1-x }$
To divide by a fraction, multiply by the reciprocal of that fraction$\left( \frac{ 3 }{ x \times \left( 1-x \right) }+\frac{ 1 }{ 1-x } \right) \times \frac{ 1-x }{ 9-{x}^{2} }$
Write all numerators above the least common denominator $x \times \left( 1-x \right)$$\frac{ 3+x }{ x \times \left( 1-x \right) } \times \frac{ 1-x }{ 9-{x}^{2} }$
Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression$\frac{ 3+x }{ x \times \left( 1-x \right) } \times \frac{ 1-x }{ \left( 3-x \right) \times \left( 3+x \right) }$
Cancel out the common factor $3+x$$\frac{ 1 }{ x \times \left( 1-x \right) } \times \frac{ 1-x }{ 3-x }$
Cancel out the common factor $1-x$$\frac{ 1 }{ x } \times \frac{ 1 }{ 3-x }$
Multiply the fractions$\frac{ 1 }{ x \times \left( 3-x \right) }$
Distribute $x$ through the parentheses$\frac{ 1 }{ 3x-{x}^{2} }$