Solve a^2-4a+4/2a-6*a^2-9/a^2+a-6

$$\frac { a ^ { 2 } - 4 a + 4 } { 2 a - 6 } \cdot \frac { a ^ { 2 } - 9 } { a ^ { 2 } + a - 6 }$$

Evaluate

$$\frac{a}{2}-1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-9}{a^{2}+a-6}.

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

Cancel out a+3 in both numerator and denominator.

$$\frac{a^{2}-4a+4}{2a-6}\times \frac{a-3}{a-2}$$

Multiply \frac{a^{2}-4a+4}{2a-6} times \frac{a-3}{a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4a+4\right)\left(a-3\right)}{\left(2a-6\right)\left(a-2\right)}$$

Factor the expressions that are not already factored.

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

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

$$\frac{a-2}{2}$$

Expand

$$\frac{a}{2}-1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-9}{a^{2}+a-6}.

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

Cancel out a+3 in both numerator and denominator.

$$\frac{a^{2}-4a+4}{2a-6}\times \frac{a-3}{a-2}$$

Multiply \frac{a^{2}-4a+4}{2a-6} times \frac{a-3}{a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4a+4\right)\left(a-3\right)}{\left(2a-6\right)\left(a-2\right)}$$

Factor the expressions that are not already factored.

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

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

$$\frac{a-2}{2}$$