Simplifying the Algebraic Expression
To divide the expression \(\frac{(-10x+50)}{(x-5)}\), we first factor the numerator.
The numerator is \(-10x + 50\). We can factor out a common factor of \(-10\):
\(-10x + 50 = -10(x - 5)\)
Performing the Division
Now substitute the factored numerator back into the original expression:
\(\frac{-10(x - 5)}{(x - 5)}\)
Since it is given that \(x \neq 5\), the term \((x - 5)\) is non-zero. Therefore, we can cancel the common factor \((x - 5)\) from the numerator and the denominator.
\(\frac{-10\cancel{(x - 5)}}{\cancel{(x - 5)}} = -10\)
The result of the division is \(-10\).
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