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.)

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UpStudy AI · Accepted Answer

To multiply the given expressions:

$$
\frac{7x - 7}{5x + 5} \cdot \frac{6x + 6}{10x - 10}
$$

**Step 1: Factor each part**

$$
\frac{7(x - 1)}{5(x + 1)} \cdot \frac{6(x + 1)}{10(x - 1)}
$$

**Step 2: Multiply the numerators and denominators**

$$
\frac{7 \cdot 6 \cdot (x - 1) \cdot (x + 1)}{5 \cdot 10 \cdot (x + 1) \cdot (x - 1)}
$$

**Step 3: Simplify by canceling common factors**

- $$ (x - 1) $$ cancels out.
- $$ (x + 1) $$ cancels out.
- $$ 7 \cdot 6 = 42 $$
- $$ 5 \cdot 10 = 50 $$

**Step 4: Reduce the fraction**

$$
\frac{42}{50} = \frac{21}{25}
$$

**Final Answer:**

$$\frac{21}{25}$$
$$\frac{21}{25}$$

Multiply.

(Type an integer or a fraction. Simplify your answer.)

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Multiply. (Type an integer or a fraction. Simplify your answer.)