Solve a^2+a-30/a^2-11a+30*a^2+2a-48/a^2+11a+30

$$\frac { a ^ { 2 } + a - 30 } { a ^ { 2 } - 11 a + 30 } \cdot \frac { a ^ { 2 } + 2 a - 48 } { a ^ { 2 } + 11 a + 30 }$$

Evaluate

$$\frac{a+8}{a+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}+a-30}{a^{2}-11a+30}.

$$\frac{\left(a-5\right)\left(a+6\right)}{\left(a-6\right)\left(a-5\right)}\times \frac{a^{2}+2a-48}{a^{2}+11a+30}$$

Cancel out a-5 in both numerator and denominator.

$$\frac{a+6}{a-6}\times \frac{a^{2}+2a-48}{a^{2}+11a+30}$$

Multiply \frac{a+6}{a-6} times \frac{a^{2}+2a-48}{a^{2}+11a+30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a+6\right)\left(a^{2}+2a-48\right)}{\left(a-6\right)\left(a^{2}+11a+30\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-6\right)\left(a+6\right)\left(a+8\right)}{\left(a-6\right)\left(a+5\right)\left(a+6\right)}$$

Cancel out \left(a-6\right)\left(a+6\right) in both numerator and denominator.

$$\frac{a+8}{a+5}$$

Expand

$$\frac{a+8}{a+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}+a-30}{a^{2}-11a+30}.

$$\frac{\left(a-5\right)\left(a+6\right)}{\left(a-6\right)\left(a-5\right)}\times \frac{a^{2}+2a-48}{a^{2}+11a+30}$$

Cancel out a-5 in both numerator and denominator.

$$\frac{a+6}{a-6}\times \frac{a^{2}+2a-48}{a^{2}+11a+30}$$

Multiply \frac{a+6}{a-6} times \frac{a^{2}+2a-48}{a^{2}+11a+30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a+6\right)\left(a^{2}+2a-48\right)}{\left(a-6\right)\left(a^{2}+11a+30\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-6\right)\left(a+6\right)\left(a+8\right)}{\left(a-6\right)\left(a+5\right)\left(a+6\right)}$$

Cancel out \left(a-6\right)\left(a+6\right) in both numerator and denominator.

$$\frac{a+8}{a+5}$$