Solve -a^2-25/a^2+10a+25diva^2-1/a+5*a^2-2a+1/a-5

$$- \frac { a ^ { 2 } - 25 } { a ^ { 2 } + 10 a + 25 } \div \frac { a ^ { 2 } - 1 } { a + 5 } \times \frac { a ^ { 2 } - 2 a + 1 } { a - 5 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-25}{a^{2}+10a+25}.

$$\frac{-\frac{\left(a-5\right)\left(a+5\right)}{\left(a+5\right)^{2}}}{\frac{a^{2}-1}{a+5}}\times \frac{a^{2}-2a+1}{a-5}$$

Cancel out a+5 in both numerator and denominator.

$$\frac{-\frac{a-5}{a+5}}{\frac{a^{2}-1}{a+5}}\times \frac{a^{2}-2a+1}{a-5}$$

Divide -\frac{a-5}{a+5} by \frac{a^{2}-1}{a+5} by multiplying -\frac{a-5}{a+5} by the reciprocal of \frac{a^{2}-1}{a+5}.

$$\frac{\left(-\frac{a-5}{a+5}\right)\left(a+5\right)}{a^{2}-1}\times \frac{a^{2}-2a+1}{a-5}$$

Cancel out a+5 and a+5.

$$\frac{-\left(a-5\right)}{a^{2}-1}\times \frac{a^{2}-2a+1}{a-5}$$

Multiply \frac{-\left(a-5\right)}{a^{2}-1} times \frac{a^{2}-2a+1}{a-5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(a-5\right)\left(a^{2}-2a+1\right)}{\left(a^{2}-1\right)\left(a-5\right)}$$

Cancel out a-5 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-25}{a^{2}+10a+25}.

$$\frac{-\frac{\left(a-5\right)\left(a+5\right)}{\left(a+5\right)^{2}}}{\frac{a^{2}-1}{a+5}}\times \frac{a^{2}-2a+1}{a-5}$$

Cancel out a+5 in both numerator and denominator.

$$\frac{-\frac{a-5}{a+5}}{\frac{a^{2}-1}{a+5}}\times \frac{a^{2}-2a+1}{a-5}$$

Divide -\frac{a-5}{a+5} by \frac{a^{2}-1}{a+5} by multiplying -\frac{a-5}{a+5} by the reciprocal of \frac{a^{2}-1}{a+5}.

$$\frac{\left(-\frac{a-5}{a+5}\right)\left(a+5\right)}{a^{2}-1}\times \frac{a^{2}-2a+1}{a-5}$$

Cancel out a+5 and a+5.

$$\frac{-\left(a-5\right)}{a^{2}-1}\times \frac{a^{2}-2a+1}{a-5}$$

Multiply \frac{-\left(a-5\right)}{a^{2}-1} times \frac{a^{2}-2a+1}{a-5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(a-5\right)\left(a^{2}-2a+1\right)}{\left(a^{2}-1\right)\left(a-5\right)}$$

Cancel out a-5 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-1 in both numerator and denominator.

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

Expand the expression.

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