Answer
$\frac{1}{(x-5)(x+3)} $.
Work Step by Step
The given expression is
$\Rightarrow \left ( \frac{5}{x-5}-\frac{2}{x+3} \right) \div (3x+25)$
The LCD of the denominators in the bracket is $(x-5)(x+3)$.
Multiply the numerator and denominator
$\Rightarrow \left ( \frac{5(x+3)}{(x-5)(x+3)}-\frac{2(x-5)}{(x-5)(x+3)} \right) \div (3x+25)$
Add numerators in the bracket
$\Rightarrow \left ( \frac{5(x+3)-2(x-5)}{(x-5)(x+3)} \right) \div (3x+25)$
Simplify.
$\Rightarrow \left ( \frac{5x+15-2x+10}{(x-5)(x+3)} \right) \div (3x+25)$
$\Rightarrow \left ( \frac{3x+25}{(x-5)(x+3)} \right) \div (3x+25)$
Invert the divisor and multiply.
$\Rightarrow \left ( \frac{3x+25}{(x-5)(x+3)} \right) \cdot \frac{1}{(3x+25)}$
Cancel common terms.
$\Rightarrow \frac{1}{(x-5)(x+3)} $.
