Solve 7a^2/7a^3+56a^2*a^2+7a-8/2

$$\frac { 7 a ^ { 2 } } { 7 a ^ { 3 } + 56 a ^ { 2 } } \cdot \frac { a ^ { 2 } + 7 a - 8 } { 2 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{7a^{2}}{7a^{3}+56a^{2}}.

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

Cancel out 7a^{2} in both numerator and denominator.

$$\frac{1}{a+8}\times \frac{a^{2}+7a-8}{2}$$

Multiply \frac{1}{a+8} times \frac{a^{2}+7a-8}{2} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(a-1\right)\left(a+8\right)}{2\left(a+8\right)}$$

Cancel out a+8 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{7a^{2}}{7a^{3}+56a^{2}}.

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

Cancel out 7a^{2} in both numerator and denominator.

$$\frac{1}{a+8}\times \frac{a^{2}+7a-8}{2}$$

Multiply \frac{1}{a+8} times \frac{a^{2}+7a-8}{2} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(a-1\right)\left(a+8\right)}{2\left(a+8\right)}$$

Cancel out a+8 in both numerator and denominator.

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