Multiply. $$ \frac{(x+4)}{(x-4)(x-5)} \cdot \frac{(x-5)(x+5)}{(x-1)(x+4)} $$

Question

UpStudy AI · Accepted Answer

To multiply the two fractions

$$
\frac{(x+4)}{(x-4)(x-5)} \cdot \frac{(x-5)(x+5)}{(x-1)(x+4)},
$$

we can start by multiplying the numerators together and the denominators together:

$$
\frac{(x+4)(x-5)(x+5)}{(x-4)(x-5)(x-1)(x+4)}.
$$

Next, we can simplify the expression by canceling out common factors in the numerator and the denominator.

1. The factor $$ (x+4) $$ appears in both the numerator and the denominator, so we can cancel it out:

$$
\frac{(x-5)(x+5)}{(x-4)(x-5)(x-1)}.
$$

2. The factor $$ (x-5) $$ also appears in both the numerator and the denominator, so we can cancel it out as well:

$$
\frac{(x+5)}{(x-4)(x-1)}.
$$

Thus, the simplified result of the multiplication is

$$
\frac{x+5}{(x-4)(x-1)}.
$$

This is the final answer.
The simplified result is $$ \frac{x+5}{(x-4)(x-1)} $$.

Multiply. \( \frac{(x+4)}{(x-4)(x-5)} \cdot \frac{(x-5)(x+5)}{(x-1)(x+4)} \)