Solve C_5^2*C_3^2*A_2^2/C_5^3*A_{3^{3}+frac{C_{5}^2*C_{3}^2*A_{3}^3}{A_{2}^2}}=

$$\frac { C _ { 5 } ^ { 2 } \cdot C _ { 3 } ^ { 2 } \cdot A _ { 2 } ^ { 2 } } { C _ { 5 } ^ { 3 } \cdot A _ { 3 } ^ { 3 } + \frac { C _ { 5 } ^ { 2 } \cdot C _ { 3 } ^ { 2 } \cdot A _ { 3 } ^ { 3 } } { A _ { 2 } ^ { 2 } } } =$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Cancel out A_{2}^{2} in both numerator and denominator.

$$\frac{combination(2,5)combination(2,3)A_{2}^{2}combination(3,5)A_{3}^{3}+A_{3}^{3}combination(2,3)combination(2,5)}{combination(3,5)A_{3}^{3}+\frac{combination(2,5)combination(2,3)A_{3}^{3}A_{2}^{2}}{A_{2}^{2}}}$$

Cancel out A_{2}^{2} in both numerator and denominator.

$$\frac{combination(2,5)combination(2,3)A_{2}^{2}combination(3,5)A_{3}^{3}+A_{3}^{3}combination(2,3)combination(2,5)}{combination(3,5)A_{3}^{3}+A_{3}^{3}combination(2,3)combination(2,5)}$$

Extract the negative sign in combination(2,5)combination(2,3)A_{2}^{2}combination(3,5)A_{3}^{3}+A_{3}^{3}combination(2,3)combination(2,5).

$$\frac{-\left(A_{3}^{3}combination(2,3)combination(2,5)+A_{3}^{3}combination(3,5)\right)}{A_{3}^{3}combination(2,3)combination(2,5)+A_{3}^{3}combination(3,5)}$$

Cancel out A_{3}^{3}combination(2,3)combination(2,5)+A_{3}^{3}combination(3,5) in both numerator and denominator.

$$-1$$