# Calculate: (25-k^2)/(k^2-10k+25)

## Expression: $\frac{ 25-{k}^{2} }{ {k}^{2}-10k+25 }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\frac{ \left( 5-k \right) \times \left( 5+k \right) }{ {k}^{2}-10k+25 }$

Use ${a}^{2}-2ab+{b}^{2}={\left( a-b \right)}^{2}$ to factor the expression

$\frac{ \left( 5-k \right) \times \left( 5+k \right) }{ {\left( k-5 \right)}^{2} }$

Factor out the negative sign from the expression and reorder the terms

$\frac{ -\left( k-5 \right) \times \left( 5+k \right) }{ {\left( k-5 \right)}^{2} }$

Cancel out the common factor $k-5$

$\frac{ -\left( 5+k \right) }{ k-5 }$

Use $\frac{ -a }{ b }=\frac{ a }{ -b }=-\frac{ a }{ b }$ to rewrite the fraction

$-\frac{ 5+k }{ k-5 }$

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