Solve a^2+17a+70/a^2+3a-10*a^2+7a-18/a^2+14a+49

$$\frac { a ^ { 2 } + 17 a + 70 } { a ^ { 2 } + 3 a - 10 } \cdot \frac { a ^ { 2 } + 7 a - 18 } { a ^ { 2 } + 14 a + 49 }$$

Evaluate

$$\frac{\left(a+9\right)\left(a+10\right)}{\left(a+5\right)\left(a+7\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+17a+70}{a^{2}+3a-10} times \frac{a^{2}+7a-18}{a^{2}+14a+49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+17a+70\right)\left(a^{2}+7a-18\right)}{\left(a^{2}+3a-10\right)\left(a^{2}+14a+49\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+7\right)\left(a+9\right)\left(a+10\right)}{\left(a-2\right)\left(a+5\right)\left(a+7\right)^{2}}$$

Cancel out \left(a-2\right)\left(a+7\right) in both numerator and denominator.

$$\frac{\left(a+9\right)\left(a+10\right)}{\left(a+5\right)\left(a+7\right)}$$

Expand the expression.

$$\frac{a^{2}+19a+90}{a^{2}+12a+35}$$

Expand

$$\frac{a^{2}+19a+90}{\left(a+5\right)\left(a+7\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+17a+70}{a^{2}+3a-10} times \frac{a^{2}+7a-18}{a^{2}+14a+49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+17a+70\right)\left(a^{2}+7a-18\right)}{\left(a^{2}+3a-10\right)\left(a^{2}+14a+49\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+7\right)\left(a+9\right)\left(a+10\right)}{\left(a-2\right)\left(a+5\right)\left(a+7\right)^{2}}$$

Cancel out \left(a-2\right)\left(a+7\right) in both numerator and denominator.

$$\frac{\left(a+9\right)\left(a+10\right)}{\left(a+5\right)\left(a+7\right)}$$

Expand the expression.

$$\frac{a^{2}+19a+90}{a^{2}+12a+35}$$