$\frac{(x-5)^2-12}{(x-5)^2+4}$

asked by guest
on Jan 26, 2025 at 1:48 am



You asked:

Evaluate the expression: \(\frac{{\left( x - 5 \right)}^{2} - 12}{{\left( x - 5 \right)}^{2} + 4}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{\left( x - 5 \right)}^{2} - 12}{{\left( x - 5 \right)}^{2} + 4} = \frac{\left(x - 5\right)^{2} - 12}{\left(x - 5\right)^{2} + 4} \)

Expanded

\[\frac{{\left( x - 5 \right)}^{2} - 12}{{\left( x - 5 \right)}^{2} + 4} = \frac{x^{2}}{x^{2} - 10 x + 29} - \frac{10 x}{x^{2} - 10 x + 29} + \frac{13}{x^{2} - 10 x + 29}\]

Factored

\[\frac{{\left( x - 5 \right)}^{2} - 12}{{\left( x - 5 \right)}^{2} + 4} = \frac{x^{2} - 10 x + 13}{x^{2} - 10 x + 29}\]

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