What is (x^2-6x+9)/(5x-15) ?

The solution to (x^2-6x+9)/(5x-15) is (x-3)/5

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simplify (x^2-6x+9)/(5x-15)

simplify

\frac{x ^{2} - 6 x + 9}{5 x - 15}

\frac{x - 3}{5}

Solution steps

\frac{x ^{2} - 6 x + 9}{5 x - 15}

Factor

x^{2} - 6 x + 9 : (x - 3)^{2}

= \frac{( x - 3 ) ^{2}}{5 x - 15}

Factor

5 x - 15 : 5 (x - 3)

= \frac{( x - 3 ) ^{2}}{5 ( x - 3 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 3)^{2} = (x - 3) (x - 3)

= \frac{( x - 3 ) ( x - 3 )}{5 ( x - 3 )}

Cancel the common factor:

x - 3

= \frac{x - 3}{5}

\frac{1}{3} \div 2

- 1 2^{2}

- 2^{- 3}

\frac{24}{4}

1 - \frac{1}{x}