Solve a^2+18a+80/a^2+4a-21*a^2+6a-27/a^2+20a+100

$$\frac { a ^ { 2 } + 18 a + 80 } { a ^ { 2 } + 4 a - 21 } \cdot \frac { a ^ { 2 } + 6 a - 27 } { a ^ { 2 } + 20 a + 100 }$$

Evaluate

$$\frac{\left(a+8\right)\left(a+9\right)}{\left(a+7\right)\left(a+10\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+18a+80}{a^{2}+4a-21} times \frac{a^{2}+6a-27}{a^{2}+20a+100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+18a+80\right)\left(a^{2}+6a-27\right)}{\left(a^{2}+4a-21\right)\left(a^{2}+20a+100\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-3\right)\left(a+8\right)\left(a+9\right)\left(a+10\right)}{\left(a-3\right)\left(a+7\right)\left(a+10\right)^{2}}$$

Cancel out \left(a-3\right)\left(a+10\right) in both numerator and denominator.

$$\frac{\left(a+8\right)\left(a+9\right)}{\left(a+7\right)\left(a+10\right)}$$

Expand the expression.

$$\frac{a^{2}+17a+72}{a^{2}+17a+70}$$

Expand

$$\frac{a^{2}+17a+72}{\left(a+7\right)\left(a+10\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+18a+80}{a^{2}+4a-21} times \frac{a^{2}+6a-27}{a^{2}+20a+100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+18a+80\right)\left(a^{2}+6a-27\right)}{\left(a^{2}+4a-21\right)\left(a^{2}+20a+100\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-3\right)\left(a+8\right)\left(a+9\right)\left(a+10\right)}{\left(a-3\right)\left(a+7\right)\left(a+10\right)^{2}}$$

Cancel out \left(a-3\right)\left(a+10\right) in both numerator and denominator.

$$\frac{\left(a+8\right)\left(a+9\right)}{\left(a+7\right)\left(a+10\right)}$$

Expand the expression.

$$\frac{a^{2}+17a+72}{a^{2}+17a+70}$$