Solve m^2-1/m^2-6m+5*m^2-10m+25/m^2-25

$$\frac { m ^ { 2 } - 1 } { m ^ { 2 } - 6 m + 5 } \times \frac { m ^ { 2 } - 10 m + 25 } { m ^ { 2 } - 25 }$$

Evaluate

$$\frac{m+1}{m+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-1}{m^{2}-6m+5}.

$$\frac{\left(m-1\right)\left(m+1\right)}{\left(m-5\right)\left(m-1\right)}\times \frac{m^{2}-10m+25}{m^{2}-25}$$

Cancel out m-1 in both numerator and denominator.

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

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

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

Cancel out m-5 in both numerator and denominator.

$$\frac{m+1}{m-5}\times \frac{m-5}{m+5}$$

Multiply \frac{m+1}{m-5} times \frac{m-5}{m+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+1\right)\left(m-5\right)}{\left(m-5\right)\left(m+5\right)}$$

Cancel out m-5 in both numerator and denominator.

$$\frac{m+1}{m+5}$$

Expand

$$\frac{m+1}{m+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-1}{m^{2}-6m+5}.

$$\frac{\left(m-1\right)\left(m+1\right)}{\left(m-5\right)\left(m-1\right)}\times \frac{m^{2}-10m+25}{m^{2}-25}$$

Cancel out m-1 in both numerator and denominator.

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

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

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

Cancel out m-5 in both numerator and denominator.

$$\frac{m+1}{m-5}\times \frac{m-5}{m+5}$$

Multiply \frac{m+1}{m-5} times \frac{m-5}{m+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+1\right)\left(m-5\right)}{\left(m-5\right)\left(m+5\right)}$$

Cancel out m-5 in both numerator and denominator.

$$\frac{m+1}{m+5}$$