Solve (a-3)^2/4-b^2*2+b/3-a*a^2/3a-9

$$\frac { ( a - 3 ) ^ { 2 } } { 4 - b ^ { 2 } } \times \frac { 2 + b } { 3 - a } \times \frac { a ^ { 2 } } { 3 a - 9 }$$

Evaluate

$$\frac{a^{2}}{3\left(b-2\right)}$$

Short Solution Steps

Multiply \frac{\left(a-3\right)^{2}}{4-b^{2}} times \frac{2+b}{3-a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-3\right)^{2}\left(2+b\right)}{\left(4-b^{2}\right)\left(3-a\right)}\times \frac{a^{2}}{3a-9}$$

Multiply \frac{\left(a-3\right)^{2}\left(2+b\right)}{\left(4-b^{2}\right)\left(3-a\right)} times \frac{a^{2}}{3a-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-3\right)^{2}\left(2+b\right)a^{2}}{\left(4-b^{2}\right)\left(3-a\right)\left(3a-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(b+2\right)a^{2}\left(a-3\right)^{2}}{3\left(a-3\right)\left(b-2\right)\left(-b-2\right)\left(-a+3\right)}$$

Extract the negative sign in 2+b.

$$\frac{-\left(-b-2\right)a^{2}\left(a-3\right)^{2}}{3\left(a-3\right)\left(b-2\right)\left(-b-2\right)\left(-a+3\right)}$$

Cancel out \left(a-3\right)\left(-b-2\right) in both numerator and denominator.

$$\frac{-\left(a-3\right)a^{2}}{3\left(b-2\right)\left(-a+3\right)}$$

Expand the expression.

$$\frac{-a^{3}+3a^{2}}{-3ab+6a+9b-18}$$

Factor the expressions that are not already factored.

$$\frac{\left(-a+3\right)a^{2}}{3\left(a-3\right)\left(-b+2\right)}$$

Extract the negative sign in 3-a.

$$\frac{-\left(a-3\right)a^{2}}{3\left(a-3\right)\left(-b+2\right)}$$

Cancel out a-3 in both numerator and denominator.

$$\frac{-a^{2}}{3\left(-b+2\right)}$$

Expand the expression.

$$\frac{-a^{2}}{-3b+6}$$

Expand

$$-\frac{a^{2}}{3\left(2-b\right)}$$

Short Solution Steps

Multiply \frac{\left(a-3\right)^{2}}{4-b^{2}} times \frac{2+b}{3-a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-3\right)^{2}\left(2+b\right)}{\left(4-b^{2}\right)\left(3-a\right)}\times \frac{a^{2}}{3a-9}$$

Multiply \frac{\left(a-3\right)^{2}\left(2+b\right)}{\left(4-b^{2}\right)\left(3-a\right)} times \frac{a^{2}}{3a-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-3\right)^{2}\left(2+b\right)a^{2}}{\left(4-b^{2}\right)\left(3-a\right)\left(3a-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(b+2\right)a^{2}\left(a-3\right)^{2}}{3\left(a-3\right)\left(b-2\right)\left(-b-2\right)\left(-a+3\right)}$$

Extract the negative sign in 2+b.

$$\frac{-\left(-b-2\right)a^{2}\left(a-3\right)^{2}}{3\left(a-3\right)\left(b-2\right)\left(-b-2\right)\left(-a+3\right)}$$

Cancel out \left(a-3\right)\left(-b-2\right) in both numerator and denominator.

$$\frac{-\left(a-3\right)a^{2}}{3\left(b-2\right)\left(-a+3\right)}$$

Expand the expression.

$$\frac{-a^{3}+3a^{2}}{-3ab+6a+9b-18}$$

Factor the expressions that are not already factored.

$$\frac{\left(-a+3\right)a^{2}}{3\left(a-3\right)\left(-b+2\right)}$$

Extract the negative sign in 3-a.

$$\frac{-\left(a-3\right)a^{2}}{3\left(a-3\right)\left(-b+2\right)}$$

Cancel out a-3 in both numerator and denominator.

$$\frac{-a^{2}}{3\left(-b+2\right)}$$

Expand the expression.

$$\frac{-a^{2}}{-3b+6}$$