Solve a^2-6a-7/a^2-1*a^2+a/a^2

$$\frac { a ^ { 2 } - 6 a - 7 } { a ^ { 2 } - 1 } \times \frac { a ^ { 2 } + a } { a ^ { 2 } }$$

Evaluate

$$\frac{\left(a-7\right)\left(a+1\right)}{a\left(a-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-6a-7}{a^{2}-1}.

$$\frac{\left(a-7\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}\times \frac{a^{2}+a}{a^{2}}$$

Cancel out a+1 in both numerator and denominator.

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

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

$$\frac{a-7}{a-1}\times \frac{a\left(a+1\right)}{a^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-7}{a-1}\times \frac{a+1}{a}$$

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

$$\frac{\left(a-7\right)\left(a+1\right)}{\left(a-1\right)a}$$

Use the distributive property to multiply a-7 by a+1 and combine like terms.

$$\frac{a^{2}-6a-7}{\left(a-1\right)a}$$

Use the distributive property to multiply a-1 by a.

$$\frac{a^{2}-6a-7}{a^{2}-a}$$

Expand

$$\frac{a^{2}-6a-7}{a\left(a-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-6a-7}{a^{2}-1}.

$$\frac{\left(a-7\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}\times \frac{a^{2}+a}{a^{2}}$$

Cancel out a+1 in both numerator and denominator.

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

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

$$\frac{a-7}{a-1}\times \frac{a\left(a+1\right)}{a^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-7}{a-1}\times \frac{a+1}{a}$$

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

$$\frac{\left(a-7\right)\left(a+1\right)}{\left(a-1\right)a}$$

Use the distributive property to multiply a-7 by a+1 and combine like terms.

$$\frac{a^{2}-6a-7}{\left(a-1\right)a}$$

Use the distributive property to multiply a-1 by a.

$$\frac{a^{2}-6a-7}{a^{2}-a}$$