Multiply. \[ \frac{7 x-7}{5 x+5} \cdot \frac{6 x+6}{10 x-10} \] \( \frac{7 x-7}{5 x+5} \cdot \frac{6 x+6}{10 x-10}=\square \) (Type an integer or a fraction. Simplify your answer.)

To simplify the expression \[ \frac{7x - 7}{5x + 5} \cdot \frac{6x + 6}{10x - 10}, \] we first factor each part. 1. For \(7x - 7\), we can factor out 7: \[ 7(x - 1). \] 2. For \(5x + 5\), we can factor out 5: \[ 5(x + 1). \] 3. For \(6x + 6\), we can factor out 6: \[ 6(x + 1). \] 4. For \(10x - 10\), we can factor out 10: \[ 10(x - 1). \] Now, we can rewrite the original expression using these factored forms: \[ \frac{7(x - 1)}{5(x + 1)} \cdot \frac{6(x + 1)}{10(x - 1)}. \] Next, we multiply: \[ = \frac{7(x - 1) \cdot 6(x + 1)}{5(x + 1) \cdot 10(x - 1)}. \] Now we can cancel out the common terms \( (x - 1) \) and \( (x + 1) \): \[ = \frac{7 \cdot 6}{5 \cdot 10} = \frac{42}{50}. \] Finally, we simplify \( \frac{42}{50} \): \[ = \frac{21}{25}. \] Thus, the simplified result is \[ \frac{21}{25}. \] So, \[ \frac{7 x-7}{5 x+5} \cdot \frac{6 x+6}{10 x-10} = \frac{21}{25}. \]